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z0{w|V8M!Qeb5n#@LElQ#POe&-=H`Ot)xUV60apti_JO5;XDd6`0dJq?ViM3qwMq`? z#EOlL?V?jMY1%VZ*9$vtNAkCC=kjh&08}?e&(D8n6)nc!L~itd?~={BUQmGlJPPnL zB75~<%@2_1Fjl=9&?B9BA$L+#+i!48*)~>zGGNb5w^aV;b zRk)hu#6^&Tugg&Ep>`oT+8?+`Vl`){mc#861C!!^gWh7p`nxXiL2Lnng+_R-2S_WS zQ>?w%vw+Y24!m>31u_SRuO3h7#Kp
    DenseAxisArray{T}(undef, axes...) where T

    Construct an uninitialized DenseAxisArray with element-type T indexed over the given axes.

    Example

    julia> array = Containers.DenseAxisArray{Float64}(undef, [:a, :b], 1:2);
+4
    source
    DenseAxisArray{T}(undef, axes...) where T

    Construct an uninitialized DenseAxisArray with element-type T indexed over the given axes.

    Example

    julia> array = Containers.DenseAxisArray{Float64}(undef, [:a, :b], 1:2);
 
 julia> fill!(array, 1.0)
 2-dimensional DenseAxisArray{Float64,2,...} with index sets:
@@ -34,7 +34,7 @@
     Dimension 2, 1:2
 And data, a 2×2 Matrix{Float64}:
  1.0  5.0
- 1.0  1.0
    source

    SparseAxisArray

    SparseAxisArray

    JuMP.Containers.SparseAxisArray — Type
    struct SparseAxisArray{T,N,K<:NTuple{N, Any}} <: AbstractArray{T,N}
     data::OrderedCollections.OrderedDict{K,T}
 end

    N-dimensional array with elements of type T where only a subset of the entries are defined. The entries with indices idx = (i1, i2, ..., iN) in keys(data) has value data[idx].

    Note that, as opposed to SparseArrays.AbstractSparseArray, the missing entries are not assumed to be zero(T), they are simply not part of the array. This means that the result of map(f, sa::SparseAxisArray) or f.(sa::SparseAxisArray) has the same sparsity structure as sa, even if f(zero(T)) is not zero.

    Example

    julia> using OrderedCollections: OrderedDict
 
@@ -51,7 +51,7 @@
   [b, 3]  =  3.0
 
 julia> array[:b, 3]
-3.0
    source

    Containers.@container

    JuMP.Containers.@container — Macro
    @container([i=..., j=..., ...], expr[, container = :Auto])

    Create a container with indices i, j, ... and values given by expr that may depend on the value of the indices.

    @container(ref[i=..., j=..., ...], expr[, container = :Auto])

    Same as above but the container is assigned to the variable of name ref.

    The type of container can be controlled by the container keyword.

    Note

    When the index set is explicitly given as 1:n for any expression n, it is transformed to Base.OneTo(n) before being given to container.

    Example

    julia> Containers.@container([i = 1:3, j = 1:3], i + j)
+3.0
    source

    Containers.@container

    JuMP.Containers.@container — Macro
    @container([i=..., j=..., ...], expr[, container = :Auto])

    Create a container with indices i, j, ... and values given by expr that may depend on the value of the indices.

    @container(ref[i=..., j=..., ...], expr[, container = :Auto])

    Same as above but the container is assigned to the variable of name ref.

    The type of container can be controlled by the container keyword.

    Note

    When the index set is explicitly given as 1:n for any expression n, it is transformed to Base.OneTo(n) before being given to container.

    Example

    julia> Containers.@container([i = 1:3, j = 1:3], i + j)
 3×3 Matrix{Int64}:
  2  3  4
  3  4  5
@@ -86,7 +86,7 @@
   [1, 3]  =  4
   [2, 2]  =  4
   [2, 3]  =  5
-  [3, 3]  =  6
    source

    Containers.container

    JuMP.Containers.container — Function
    container(f::Function, indices[[, ::Type{C} = AutoContainerType], names])

    Create a container of type C with index names names, indices indices and values at given indices given by f.

    If the method with names is not specialized on Type{C}, it falls back to calling container(f, indices, c) for backwards compatibility with containers not supporting index names.

    Example

    julia> Containers.container((i, j) -> i + j, Containers.vectorized_product(Base.OneTo(3), Base.OneTo(3)))
+  [3, 3]  =  6
    source

    Containers.container

    JuMP.Containers.container — Function
    container(f::Function, indices[[, ::Type{C} = AutoContainerType], names])

    Create a container of type C with index names names, indices indices and values at given indices given by f.

    If the method with names is not specialized on Type{C}, it falls back to calling container(f, indices, c) for backwards compatibility with containers not supporting index names.

    Example

    julia> Containers.container((i, j) -> i + j, Containers.vectorized_product(Base.OneTo(3), Base.OneTo(3)))
 3×3 Matrix{Int64}:
  2  3  4
  3  4  5
@@ -115,7 +115,7 @@
   [1, 2]  =  3
   [1, 3]  =  4
   [2, 3]  =  5
-  [3, 3]  =  6
    source

    Containers.rowtable

    JuMP.Containers.rowtable — Function
    rowtable([f::Function=identity,] x; [header::Vector{Symbol} = Symbol[]])

    Applies the function f to all elements of the variable container x, returning the result as a Vector of NamedTuples, where header is a vector containing the corresponding axis names.

    If x is an N-dimensional array, there must be N+1 names, so that the last name corresponds to the result of f(x[i]).

    If header is left empty, then the default header is [:x1, :x2, ..., :xN, :y].

    Info

    A Vector of NamedTuples implements the Tables.jl interface, and so the result can be used as input for any function that consumes a 'Tables.jl' compatible source.

    Example

    julia> model = Model();
+  [3, 3]  =  6
    source

    Containers.rowtable

    JuMP.Containers.rowtable — Function
    rowtable([f::Function=identity,] x; [header::Vector{Symbol} = Symbol[]])

    Applies the function f to all elements of the variable container x, returning the result as a Vector of NamedTuples, where header is a vector containing the corresponding axis names.

    If x is an N-dimensional array, there must be N+1 names, so that the last name corresponds to the result of f(x[i]).

    If header is left empty, then the default header is [:x1, :x2, ..., :xN, :y].

    Info

    A Vector of NamedTuples implements the Tables.jl interface, and so the result can be used as input for any function that consumes a 'Tables.jl' compatible source.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[i=1:2, j=i:2] >= 0, start = i+j);
 
@@ -129,7 +129,7 @@
 3-element Vector{@NamedTuple{x1::Int64, x2::Int64, y::VariableRef}}:
  (x1 = 1, x2 = 1, y = x[1,1])
  (x1 = 1, x2 = 2, y = x[1,2])
- (x1 = 2, x2 = 2, y = x[2,2])
    source

    Containers.default_container

    Containers.nested

    Containers.default_container

    Containers.nested

    JuMP.Containers.nested — Function
    nested(iterators...; condition = (args...) -> true)

    Create a NestedIterator.

    Example

    julia> iterator = Containers.nested(
            () -> 1:2,
            (i,) -> ["A", "B"];
            condition = (i, j) -> isodd(i) || j == "B",
@@ -139,21 +139,21 @@
 3-element Vector{Tuple{Int64, String}}:
  (1, "A")
  (1, "B")
- (2, "B")
    source

    Containers.vectorized_product

    Containers.vectorized_product

    Containers.build_error_fn

    JuMP.Containers.build_error_fn — Function
    build_error_fn(macro_name, args, source)

    Return a function that can be used in place of Base.error, but which additionally prints the macro from which it was called.

    source

    Containers.parse_macro_arguments

    Containers.build_error_fn

    JuMP.Containers.build_error_fn — Function
    build_error_fn(macro_name, args, source)

    Return a function that can be used in place of Base.error, but which additionally prints the macro from which it was called.

    source

    Containers.parse_macro_arguments

    JuMP.Containers.parse_macro_arguments — Function
    parse_macro_arguments(
     error_fn::Function,
     args;
     valid_kwargs::Union{Nothing,Vector{Symbol}} = nothing,
     num_positional_args::Union{Nothing,Int,UnitRange{Int}} = nothing,
-)

    Returns a Tuple{Vector{Any},Dict{Symbol,Any}} containing the ordered positional arguments and a dictionary mapping the keyword arguments.

    This specially handles the distinction of @foo(key = value) and @foo(; key = value) in macros.

    An error is thrown if multiple keyword arguments are passed with the same key.

    If valid_kwargs is a Vector{Symbol}, an error is thrown if a keyword is not in valid_kwargs.

    If num_positional_args is not nothing, an error is thrown if the number of positional arguments is not in num_positional_args.

    source

    Containers.parse_ref_sets

    JuMP.Containers.parse_ref_sets — Function
    parse_ref_sets(
+)

    Returns a Tuple{Vector{Any},Dict{Symbol,Any}} containing the ordered positional arguments and a dictionary mapping the keyword arguments.

    This specially handles the distinction of @foo(key = value) and @foo(; key = value) in macros.

    An error is thrown if multiple keyword arguments are passed with the same key.

    If valid_kwargs is a Vector{Symbol}, an error is thrown if a keyword is not in valid_kwargs.

    If num_positional_args is not nothing, an error is thrown if the number of positional arguments is not in num_positional_args.

    source

    Containers.parse_ref_sets

    JuMP.Containers.parse_ref_sets — Function
    parse_ref_sets(
     error_fn::Function,
     expr;
     invalid_index_variables::Vector{Symbol} = Symbol[],
-)

    Helper function for macros to construct container objects.

    Warning

    This function is for advanced users implementing JuMP extensions. See container_code for more details.

    Arguments

    • error_fn: a function that takes a String and throws an error, potentially annotating the input string with extra information such as from which macro it was thrown from. Use error if you do not want a modified error message.
    • expr: an Expr that specifies the container, for example, :(x[i = 1:3, [:red, :blue], k = S; i + k <= 6])

    Returns

    1. name: the name of the container, if given, otherwise nothing
    2. index_vars: a Vector{Any} of names for the index variables, for example, [:i, gensym(), :k]. These may also be expressions, like :((i, j)) from a call like :(x[(i, j) in S]).
    3. indices: an iterator over the indices, for example, Containers.NestedIterator

    Example

    See container_code for a worked example.

    source

    Containers.build_name_expr

    JuMP.Containers.build_name_expr — Function
    build_name_expr(
+)

    Helper function for macros to construct container objects.

    Warning

    This function is for advanced users implementing JuMP extensions. See container_code for more details.

    Arguments

    • error_fn: a function that takes a String and throws an error, potentially annotating the input string with extra information such as from which macro it was thrown from. Use error if you do not want a modified error message.
    • expr: an Expr that specifies the container, for example, :(x[i = 1:3, [:red, :blue], k = S; i + k <= 6])

    Returns

    1. name: the name of the container, if given, otherwise nothing
    2. index_vars: a Vector{Any} of names for the index variables, for example, [:i, gensym(), :k]. These may also be expressions, like :((i, j)) from a call like :(x[(i, j) in S]).
    3. indices: an iterator over the indices, for example, Containers.NestedIterator

    Example

    See container_code for a worked example.

    source

    Containers.build_name_expr

    JuMP.Containers.build_name_expr — Function
    build_name_expr(
     name::Union{Symbol,Nothing},
     index_vars::Vector,
     kwargs::Dict{Symbol,Any},
@@ -164,12 +164,12 @@
 ""
 
 julia> Containers.build_name_expr(:y, [:i, :j], Dict{Symbol,Any}(:base_name => "y"))
-:(string("y", "[", string($(Expr(:escape, :i))), ",", string($(Expr(:escape, :j))), "]"))
    source

    Containers.add_additional_args

    Containers.add_additional_args

    JuMP.Containers.add_additional_args — Function
    add_additional_args(
     call::Expr,
     args::Vector,
     kwargs::Dict{Symbol,Any};
     kwarg_exclude::Vector{Symbol} = Symbol[],
-)

    Add the positional arguments args to the function call expression call, escaping each argument expression.

    This function is able to incorporate additional positional arguments to calls that already have keyword arguments.

    source

    Containers.container_code

    JuMP.Containers.container_code — Function
    container_code(
+)

    Add the positional arguments args to the function call expression call, escaping each argument expression.

    This function is able to incorporate additional positional arguments to calls that already have keyword arguments.

    source

    Containers.container_code

    JuMP.Containers.container_code — Function
    container_code(
     index_vars::Vector{Any},
     indices::Expr,
     code,
@@ -194,7 +194,7 @@
     Dimension 2, ["A", "B"]
 And data, a 2×2 Matrix{String}:
  "A"   "B"
- "AA"  "BB"
    source

    Containers.AutoContainerType

    Containers.NestedIterator

    Containers.AutoContainerType

    Containers.NestedIterator

    JuMP.Containers.NestedIterator — Type
    struct NestedIterator{T}
     iterators::T # Tuple of functions
     condition::Function
 end

    Iterators over the tuples that are produced by a nested for loop.

    Construct a NestedIterator using nested.

    Example

    julia> iterators = (() -> 1:2, (i,) -> ["A", "B"]);
@@ -217,6 +217,6 @@
        end
 (1, "A")
 (1, "B")
-(2, "B")
    source

    Containers.VectorizedProductIterator

    Containers.VectorizedProductIterator

    +end

    A wrapper type for Iterators.ProuctIterator that discards shape information and returns a Vector.

    Construct a VectorizedProductIterator using vectorized_product.

    source diff --git a/previews/PR3913/api/JuMP/index.html b/previews/PR3913/api/JuMP/index.html index 1210c03393a..31b7fdb6d22 100644 --- a/previews/PR3913/api/JuMP/index.html +++ b/previews/PR3913/api/JuMP/index.html @@ -15,7 +15,7 @@ julia> @build_constraint(x .>= 0) 2-element Vector{ScalarConstraint{AffExpr, MathOptInterface.GreaterThan{Float64}}}: ScalarConstraint{AffExpr, MathOptInterface.GreaterThan{Float64}}(x[1], MathOptInterface.GreaterThan{Float64}(-0.0)) - ScalarConstraint{AffExpr, MathOptInterface.GreaterThan{Float64}}(x[2], MathOptInterface.GreaterThan{Float64}(-0.0))source

    @constraint

    JuMP.@constraint — Macro
    @constraint(model, expr, args...; kwargs...)
+ ScalarConstraint{AffExpr, MathOptInterface.GreaterThan{Float64}}(x[2], MathOptInterface.GreaterThan{Float64}(-0.0))
    source

    @constraint

    JuMP.@constraint — Macro
    @constraint(model, expr, args...; kwargs...)
 @constraint(model, [index_sets...], expr, args...; kwargs...)
 @constraint(model, name, expr, args...; kwargs...)
 @constraint(model, name[index_sets...], expr, args...; kwargs...)

    Add a constraint described by the expression expr.

    The name argument is optional. If index sets are passed, a container is built and the constraint may depend on the indices of the index sets.

    The expression expr may be one of following forms:

    • func in set, constraining the function func to belong to the set set, which is either a MOI.AbstractSet or one of the JuMP shortcuts like SecondOrderCone or PSDCone

    • a <op> b, where <op> is one of ==, ≥, >=, ≤, <=

    • l <= f <= u or u >= f >= l, constraining the expression f to lie between l and u

    • f(x) ⟂ x, which defines a complementarity constraint

    • z --> {expr}, which defines an indicator constraint that activates when z is 1

    • !z --> {expr}, which defines an indicator constraint that activates when z is 0

    • z <--> {expr}, which defines a reified constraint

    • expr := rhs, which defines a Boolean equality constraint

    Broadcasted comparison operators like .== are also supported for the case when the left- and right-hand sides of the comparison operator are arrays.

    JuMP extensions may additionally provide support for constraint expressions which are not listed here.

    Keyword arguments

    • base_name: sets the name prefix used to generate constraint names. It corresponds to the constraint name for scalar constraints, otherwise, the constraint names are set to base_name[...] for each index ....

    • container = :Auto: force the container type by passing container = Array,

    container = DenseAxisArray, container = SparseAxisArray, or any another container type which is supported by a JuMP extension.

    • set_string_name::Bool = true: control whether to set the MOI.ConstraintName attribute. Passing set_string_name = false can improve performance.

    Other keyword arguments may be supported by JuMP extensions.

    Example

    julia> model = Model();
@@ -52,7 +52,7 @@
 z --> {x[1] ≥ 0}
 
 julia> @constraint(model, !z --> {2 * x[2] <= 3})
-!z --> {2 x[2] ≤ 3}
    source

    @constraints

    JuMP.@constraints — Macro
    @constraints(model, args...)

    Adds groups of constraints at once, in the same fashion as the @constraint macro.

    The model must be the first argument, and multiple constraints can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the constraints that were defined.

    Example

    julia> model = Model();
+!z --> {2 x[2] ≤ 3}
    source

    @constraints

    JuMP.@constraints — Macro
    @constraints(model, args...)

    Adds groups of constraints at once, in the same fashion as the @constraint macro.

    The model must be the first argument, and multiple constraints can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the constraints that were defined.

    Example

    julia> model = Model();
 
 julia> @variable(model, w);
 
@@ -75,7 +75,7 @@
  sum_to_one[2] : y + z[2] = 1
  sum_to_one[3] : y + z[3] = 1
  x ≥ 1
- -w + y ≤ 2
    source

    @expression

    @expression

    JuMP.@expression — Macro
    @expression(model::GenericModel, expression)
 @expression(model::GenericModel, [index_sets...], expression)
 @expression(model::GenericModel, name, expression)
 @expression(model::GenericModel, name[index_sets...], expression)

    Efficiently builds and returns an expression.

    The name argument is optional. If index sets are passed, a container is built and the expression may depend on the indices of the index sets.

    Keyword arguments

    • container = :Auto: force the container type by passing container = Array, container = DenseAxisArray, container = SparseAxisArray, or any another container type which is supported by a JuMP extension.

    Example

    julia> model = Model();
@@ -102,7 +102,7 @@
 3-element Vector{AffExpr}:
  x[1] + x[2] + x[3]
  2 x[1] + 2 x[2] + 2 x[3]
- 3 x[1] + 3 x[2] + 3 x[3]
    source

    @expressions

    JuMP.@expressions — Macro
    @expressions(model, args...)

    Adds multiple expressions to model at once, in the same fashion as the @expression macro.

    The model must be the first argument, and multiple expressions can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the expressions that were defined.

    Example

    julia> model = Model();
+ 3 x[1] + 3 x[2] + 3 x[3]
    source

    @expressions

    JuMP.@expressions — Macro
    @expressions(model, args...)

    Adds multiple expressions to model at once, in the same fashion as the @expression macro.

    The model must be the first argument, and multiple expressions can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the expressions that were defined.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -116,7 +116,7 @@
            my_expr, x^2 + y^2
            my_expr_1[i = 1:2], a[i] - z[i]
        end)
-(x² + y², AffExpr[-z[1] + 4, -z[2] + 5])
    source

    @force_nonlinear

    JuMP.@force_nonlinear — Macro
    @force_nonlinear(expr)

    Change the parsing of expr to construct GenericNonlinearExpr instead of GenericAffExpr or GenericQuadExpr.

    This macro works by walking expr and substituting all calls to +, -, *, /, and ^ in favor of ones that construct GenericNonlinearExpr.

    This macro will error if the resulting expression does not produce a GenericNonlinearExpr because, for example, it is used on an expression that does not use the basic arithmetic operators.

    When to use this macro

    In most cases, you should not use this macro.

    Use this macro only if the intended output type is a GenericNonlinearExpr and the regular macro calls destroy problem structure, or in rare cases, if the regular macro calls introduce a large amount of intermediate variables, for example, because they promote types to a common quadratic expression.

    Example

    Use-case one: preserve problem structure.

    julia> model = Model();
+(x² + y², AffExpr[-z[1] + 4, -z[2] + 5])
    source

    @force_nonlinear

    JuMP.@force_nonlinear — Macro
    @force_nonlinear(expr)

    Change the parsing of expr to construct GenericNonlinearExpr instead of GenericAffExpr or GenericQuadExpr.

    This macro works by walking expr and substituting all calls to +, -, *, /, and ^ in favor of ones that construct GenericNonlinearExpr.

    This macro will error if the resulting expression does not produce a GenericNonlinearExpr because, for example, it is used on an expression that does not use the basic arithmetic operators.

    When to use this macro

    In most cases, you should not use this macro.

    Use this macro only if the intended output type is a GenericNonlinearExpr and the regular macro calls destroy problem structure, or in rare cases, if the regular macro calls introduce a large amount of intermediate variables, for example, because they promote types to a common quadratic expression.

    Example

    Use-case one: preserve problem structure.

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -144,7 +144,7 @@
 2576
 
 julia> @allocated @expression(model, @force_nonlinear(x * 2.0 * (1 + x) * x))
-672
    source

    @objective

    JuMP.@objective — Macro
    @objective(model::GenericModel, sense, func)

    Set the objective sense to sense and objective function to func.

    The objective sense can be either Min, Max, MOI.MIN_SENSE, MOI.MAX_SENSE or MOI.FEASIBILITY_SENSE. In order to set the sense programmatically, that is, when sense is a variable whose value is the sense, one of the three MOI.OptimizationSense values must be used.

    Example

    Minimize the value of the variable x, do:

    julia> model = Model();
+672
    source

    @objective

    JuMP.@objective — Macro
    @objective(model::GenericModel, sense, func)

    Set the objective sense to sense and objective function to func.

    The objective sense can be either Min, Max, MOI.MIN_SENSE, MOI.MAX_SENSE or MOI.FEASIBILITY_SENSE. In order to set the sense programmatically, that is, when sense is a variable whose value is the sense, one of the three MOI.OptimizationSense values must be used.

    Example

    Minimize the value of the variable x, do:

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -165,7 +165,7 @@
 MIN_SENSE::OptimizationSense = 0
 
 julia> @objective(model, sense, x^2 - 2x + 1)
-x² - 2 x + 1
    source

    @operator

    JuMP.@operator — Macro
    @operator(model, operator, dim, f[, ∇f[, ∇²f]])

    Add the nonlinear operator operator in model with dim arguments, and create a new NonlinearOperator object called operator in the current scope.

    The function f evaluates the operator and must return a scalar.

    The optional function ∇f evaluates the first derivative, and the optional function ∇²f evaluates the second derivative.

    ∇²f may be provided only if ∇f is also provided.

    Univariate syntax

    If dim == 1, then the method signatures of each function must be:

    • f(::T)::T where {T<:Real}
    • ∇f(::T)::T where {T<:Real}
    • ∇²f(::T)::T where {T<:Real}

    Multivariate syntax

    If dim > 1, then the method signatures of each function must be:

    • f(x::T...)::T where {T<:Real}
    • ∇f(g::AbstractVector{T}, x::T...)::Nothing where {T<:Real}
    • ∇²f(H::AbstractMatrix{T}, x::T...)::Nothing where {T<:Real}

    Where the gradient vector g and Hessian matrix H are filled in-place. For the Hessian, you must fill in the non-zero lower-triangular entries only. Setting an off-diagonal upper-triangular element may error.

    Example

    julia> model = Model();
+x² - 2 x + 1
    source

    @operator

    JuMP.@operator — Macro
    @operator(model, operator, dim, f[, ∇f[, ∇²f]])

    Add the nonlinear operator operator in model with dim arguments, and create a new NonlinearOperator object called operator in the current scope.

    The function f evaluates the operator and must return a scalar.

    The optional function ∇f evaluates the first derivative, and the optional function ∇²f evaluates the second derivative.

    ∇²f may be provided only if ∇f is also provided.

    Univariate syntax

    If dim == 1, then the method signatures of each function must be:

    • f(::T)::T where {T<:Real}
    • ∇f(::T)::T where {T<:Real}
    • ∇²f(::T)::T where {T<:Real}

    Multivariate syntax

    If dim > 1, then the method signatures of each function must be:

    • f(x::T...)::T where {T<:Real}
    • ∇f(g::AbstractVector{T}, x::T...)::Nothing where {T<:Real}
    • ∇²f(H::AbstractMatrix{T}, x::T...)::Nothing where {T<:Real}

    Where the gradient vector g and Hessian matrix H are filled in-place. For the Hessian, you must fill in the non-zero lower-triangular entries only. Setting an off-diagonal upper-triangular element may error.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -204,7 +204,7 @@
 f (generic function with 1 method)
 
 julia> op_f = model[:op_f] = add_nonlinear_operator(model, 1, f; name = :op_f)
-NonlinearOperator(f, :op_f)
    source

    @variable

    JuMP.@variable — Macro
    @variable(model, expr, args..., kw_args...)

    Add a variable to the model model described by the expression expr, the positional arguments args and the keyword arguments kw_args.

    Anonymous and named variables

    expr must be one of the forms:

    • Omitted, like @variable(model), which creates an anonymous variable
    • A single symbol like @variable(model, x)
    • A container expression like @variable(model, x[i=1:3])
    • An anonymous container expression like @variable(model, [i=1:3])

    Bounds

    In addition, the expression can have bounds, such as:

    • @variable(model, x >= 0)
    • @variable(model, x <= 0)
    • @variable(model, x == 0)
    • @variable(model, 0 <= x <= 1)

    and bounds can depend on the indices of the container expressions:

    • @variable(model, -i <= x[i=1:3] <= i)

    Sets

    You can explicitly specify the set to which the variable belongs:

    • @variable(model, x in MOI.Interval(0.0, 1.0))

    For more information on this syntax, read Variables constrained on creation.

    Positional arguments

    The recognized positional arguments in args are the following:

    • Bin: restricts the variable to the MOI.ZeroOne set, that is, {0, 1}. For example, @variable(model, x, Bin). Note: you cannot use @variable(model, Bin), use the binary keyword instead.
    • Int: restricts the variable to the set of integers, that is, ..., -2, -1, 0, 1, 2, ... For example, @variable(model, x, Int). Note: you cannot use @variable(model, Int), use the integer keyword instead.
    • Symmetric: Only available when creating a square matrix of variables, that is when expr is of the form varname[1:n,1:n] or varname[i=1:n,j=1:n], it creates a symmetric matrix of variables.
    • PSD: A restrictive extension to Symmetric which constraints a square matrix of variables to Symmetric and constrains to be positive semidefinite.

    Keyword arguments

    Four keyword arguments are useful in all cases:

    • base_name: Sets the name prefix used to generate variable names. It corresponds to the variable name for scalar variable, otherwise, the variable names are set to base_name[...] for each index ... of the axes axes.
    • start::Float64: specify the value passed to set_start_value for each variable
    • container: specify the container type. See Forcing the container type for more information.
    • set_string_name::Bool = true: control whether to set the MOI.VariableName attribute. Passing set_string_name = false can improve performance.

    Other keyword arguments are needed to disambiguate sitations with anonymous variables:

    • lower_bound::Float64: an alternative to x >= lb, sets the value of the variable lower bound.
    • upper_bound::Float64: an alternative to x <= ub, sets the value of the variable upper bound.
    • binary::Bool: an alternative to passing Bin, sets whether the variable is binary or not.
    • integer::Bool: an alternative to passing Int, sets whether the variable is integer or not.
    • set::MOI.AbstractSet: an alternative to using x in set
    • variable_type: used by JuMP extensions. See Extend @variable for more information.

    Example

    The following are equivalent ways of creating a variable x of name x with lower bound 0:

    julia> model = Model();
+NonlinearOperator(f, :op_f)
    source

    @variable

    JuMP.@variable — Macro
    @variable(model, expr, args..., kw_args...)

    Add a variable to the model model described by the expression expr, the positional arguments args and the keyword arguments kw_args.

    Anonymous and named variables

    expr must be one of the forms:

    • Omitted, like @variable(model), which creates an anonymous variable
    • A single symbol like @variable(model, x)
    • A container expression like @variable(model, x[i=1:3])
    • An anonymous container expression like @variable(model, [i=1:3])

    Bounds

    In addition, the expression can have bounds, such as:

    • @variable(model, x >= 0)
    • @variable(model, x <= 0)
    • @variable(model, x == 0)
    • @variable(model, 0 <= x <= 1)

    and bounds can depend on the indices of the container expressions:

    • @variable(model, -i <= x[i=1:3] <= i)

    Sets

    You can explicitly specify the set to which the variable belongs:

    • @variable(model, x in MOI.Interval(0.0, 1.0))

    For more information on this syntax, read Variables constrained on creation.

    Positional arguments

    The recognized positional arguments in args are the following:

    • Bin: restricts the variable to the MOI.ZeroOne set, that is, {0, 1}. For example, @variable(model, x, Bin). Note: you cannot use @variable(model, Bin), use the binary keyword instead.
    • Int: restricts the variable to the set of integers, that is, ..., -2, -1, 0, 1, 2, ... For example, @variable(model, x, Int). Note: you cannot use @variable(model, Int), use the integer keyword instead.
    • Symmetric: Only available when creating a square matrix of variables, that is when expr is of the form varname[1:n,1:n] or varname[i=1:n,j=1:n], it creates a symmetric matrix of variables.
    • PSD: A restrictive extension to Symmetric which constraints a square matrix of variables to Symmetric and constrains to be positive semidefinite.

    Keyword arguments

    Four keyword arguments are useful in all cases:

    • base_name: Sets the name prefix used to generate variable names. It corresponds to the variable name for scalar variable, otherwise, the variable names are set to base_name[...] for each index ... of the axes axes.
    • start::Float64: specify the value passed to set_start_value for each variable
    • container: specify the container type. See Forcing the container type for more information.
    • set_string_name::Bool = true: control whether to set the MOI.VariableName attribute. Passing set_string_name = false can improve performance.

    Other keyword arguments are needed to disambiguate sitations with anonymous variables:

    • lower_bound::Float64: an alternative to x >= lb, sets the value of the variable lower bound.
    • upper_bound::Float64: an alternative to x <= ub, sets the value of the variable upper bound.
    • binary::Bool: an alternative to passing Bin, sets whether the variable is binary or not.
    • integer::Bool: an alternative to passing Int, sets whether the variable is integer or not.
    • set::MOI.AbstractSet: an alternative to using x in set
    • variable_type: used by JuMP extensions. See Extend @variable for more information.

    Example

    The following are equivalent ways of creating a variable x of name x with lower bound 0:

    julia> model = Model();
 
 julia> @variable(model, x >= 0)
 x
    julia> model = Model();
@@ -233,14 +233,14 @@
 3-element Vector{VariableRef}:
  _[7]
  _[8]
- _[9]
    source

    @variables

    JuMP.@variables — Macro
    @variables(model, args...)

    Adds multiple variables to model at once, in the same fashion as the @variable macro.

    The model must be the first argument, and multiple variables can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the variables that were defined.

    Example

    julia> model = Model();
+ _[9]
    source

    @variables

    JuMP.@variables — Macro
    @variables(model, args...)

    Adds multiple variables to model at once, in the same fashion as the @variable macro.

    The model must be the first argument, and multiple variables can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the variables that were defined.

    Example

    julia> model = Model();
 
 julia> @variables(model, begin
            x
            y[i = 1:2] >= 0, (start = i)
            z, Bin, (start = 0, base_name = "Z")
        end)
-(x, VariableRef[y[1], y[2]], Z)
    Note

    Keyword arguments must be contained within parentheses (refer to the example above).

    source

    add_bridge

    JuMP.add_bridge — Function
    add_bridge(
+(x, VariableRef[y[1], y[2]], Z)
    Note

    Keyword arguments must be contained within parentheses (refer to the example above).

    source

    add_bridge

    JuMP.add_bridge — Function
    add_bridge(
     model::GenericModel{T},
     BT::Type{<:MOI.Bridges.AbstractBridge};
     coefficient_type::Type{S} = T,
@@ -252,11 +252,11 @@
            model,
            MOI.Bridges.Constraint.NumberConversionBridge;
            coefficient_type = Complex{Float64}
-       )
    source

    add_constraint

    add_constraint

    JuMP.add_constraint — Function
    add_constraint(
     model::GenericModel,
     con::AbstractConstraint,
     name::String= "",
-)

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    add_nonlinear_operator

    JuMP.add_nonlinear_operator — Function
    add_nonlinear_operator(
+)

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    add_nonlinear_operator

    add_to_expression!

    JuMP.add_to_expression! — Function
    add_to_expression!(expression, terms...)

    Updates expression in-place to expression + (*)(terms...).

    This is typically much more efficient than expression += (*)(terms...) because it avoids the temorary allocation of the right-hand side term.

    For example, add_to_expression!(expression, a, b) produces the same result as expression += a*b, and add_to_expression!(expression, a) produces the same result as expression += a.

    When to implement

    Only a few methods are defined, mostly for internal use, and only for the cases when:

    1. they can be implemented efficiently
    2. expression is capable of storing the result. For example, add_to_expression!(::AffExpr, ::GenericVariableRef, ::GenericVariableRef) is not defined because a GenericAffExpr cannot store the product of two variables.

    Example

    julia> model = Model();
+4.0
    source

    add_to_expression!

    JuMP.add_to_expression! — Function
    add_to_expression!(expression, terms...)

    Updates expression in-place to expression + (*)(terms...).

    This is typically much more efficient than expression += (*)(terms...) because it avoids the temorary allocation of the right-hand side term.

    For example, add_to_expression!(expression, a, b) produces the same result as expression += a*b, and add_to_expression!(expression, a) produces the same result as expression += a.

    When to implement

    Only a few methods are defined, mostly for internal use, and only for the cases when:

    1. they can be implemented efficiently
    2. expression is capable of storing the result. For example, add_to_expression!(::AffExpr, ::GenericVariableRef, ::GenericVariableRef) is not defined because a GenericAffExpr cannot store the product of two variables.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -316,7 +316,7 @@
 3 x[1] + 3 x[2]
 
 julia> ex2
-2 x[1] + 2 x[2]
    source

    add_to_function_constant

    JuMP.add_to_function_constant — Function
    add_to_function_constant(constraint::ConstraintRef, value)

    Add value to the function constant term of constraint.

    Note that for scalar constraints, JuMP will aggregate all constant terms onto the right-hand side of the constraint so instead of modifying the function, the set will be translated by -value. For example, given a constraint 2x <= 3, add_to_function_constant(c, 4) will modify it to 2x <= -1.

    Example

    For scalar constraints, the set is translated by -value:

    julia> model = Model();
+2 x[1] + 2 x[2]
    source

    add_to_function_constant

    JuMP.add_to_function_constant — Function
    add_to_function_constant(constraint::ConstraintRef, value)

    Add value to the function constant term of constraint.

    Note that for scalar constraints, JuMP will aggregate all constant terms onto the right-hand side of the constraint so instead of modifying the function, the set will be translated by -value. For example, given a constraint 2x <= 3, add_to_function_constant(c, 4) will modify it to 2x <= -1.

    Example

    For scalar constraints, the set is translated by -value:

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -338,7 +338,7 @@
 julia> add_to_function_constant(con, [1, 2, 2])
 
 julia> con
-con : [x + y + 1, x + 2, y + 2] ∈ MathOptInterface.SecondOrderCone(3)
    source

    add_variable

    JuMP.add_variable — Function
    add_variable(m::GenericModel, v::AbstractVariable, name::String = "")

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    all_constraints

    JuMP.all_constraints — Function
    all_constraints(model::GenericModel, function_type, set_type)::Vector{<:ConstraintRef}

    Return a list of all constraints currently in the model where the function has type function_type and the set has type set_type. The constraints are ordered by creation time.

    See also list_of_constraint_types and num_constraints.

    Example

    julia> model = Model();
+con : [x + y + 1, x + 2, y + 2] ∈ MathOptInterface.SecondOrderCone(3)
    source

    add_variable

    JuMP.add_variable — Function
    add_variable(m::GenericModel, v::AbstractVariable, name::String = "")

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    all_constraints

    JuMP.all_constraints — Function
    all_constraints(model::GenericModel, function_type, set_type)::Vector{<:ConstraintRef}

    Return a list of all constraints currently in the model where the function has type function_type and the set has type set_type. The constraints are ordered by creation time.

    See also list_of_constraint_types and num_constraints.

    Example

    julia> model = Model();
 
 julia> @variable(model, x >= 0, Bin);
 
@@ -354,7 +354,7 @@
 
 julia> all_constraints(model, AffExpr, MOI.LessThan{Float64})
 1-element Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.LessThan{Float64}}, ScalarShape}}:
- 2 x ≤ 1
    source
    all_constraints(
+ 2 x ≤ 1
    source
    all_constraints(
     model::GenericModel;
     include_variable_in_set_constraints::Bool,
 )::Vector{ConstraintRef}

    Return a list of all constraints in model.

    If include_variable_in_set_constraints == true, then VariableRef constraints such as VariableRef-in-Integer are included. To return only the structural constraints (for example, the rows in the constraint matrix of a linear program), pass include_variable_in_set_constraints = false.

    Example

    julia> model = Model();
@@ -375,7 +375,7 @@
 julia> all_constraints(model; include_variable_in_set_constraints = false)
 2-element Vector{ConstraintRef}:
  2 x ≤ 1
- x ^ 2.0 - 1.0 ≤ 0

    Performance considerations

    Note that this function is type-unstable because it returns an abstractly typed vector. If performance is a problem, consider using list_of_constraint_types and a function barrier. See the Performance tips for extensions section of the documentation for more details.

    source

    all_variables

    JuMP.all_variables — Function
    all_variables(model::GenericModel{T})::Vector{GenericVariableRef{T}} where {T}

    Returns a list of all variables currently in the model. The variables are ordered by creation time.

    Example

    julia> model = Model();
+ x ^ 2.0 - 1.0 ≤ 0

    Performance considerations

    Note that this function is type-unstable because it returns an abstractly typed vector. If performance is a problem, consider using list_of_constraint_types and a function barrier. See the Performance tips for extensions section of the documentation for more details.

    source

    all_variables

    JuMP.all_variables — Function
    all_variables(model::GenericModel{T})::Vector{GenericVariableRef{T}} where {T}

    Returns a list of all variables currently in the model. The variables are ordered by creation time.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -384,12 +384,12 @@
 julia> all_variables(model)
 2-element Vector{VariableRef}:
  x
- y
    source

    anonymous_name

    JuMP.anonymous_name — Function
    anonymous_name(::MIME, x::AbstractVariableRef)

    The name to use for an anonymous variable x when printing.

    Example

    julia> model = Model();
+ y
    source

    anonymous_name

    JuMP.anonymous_name — Function
    anonymous_name(::MIME, x::AbstractVariableRef)

    The name to use for an anonymous variable x when printing.

    Example

    julia> model = Model();
 
 julia> x = @variable(model);
 
 julia> anonymous_name(MIME("text/plain"), x)
-"_[1]"
    source

    backend

    JuMP.backend — Function
    backend(model::GenericModel)

    Return the lower-level MathOptInterface model that sits underneath JuMP. This model depends on which operating mode JuMP is in (see mode).

    • If JuMP is in DIRECT mode (that is, the model was created using direct_model), the backend will be the optimizer passed to direct_model.
    • If JuMP is in MANUAL or AUTOMATIC mode, the backend is a MOI.Utilities.CachingOptimizer.

    Use index to get the index of a variable or constraint in the backend model.

    Warning

    This function should only be used by advanced users looking to access low-level MathOptInterface or solver-specific functionality.

    Notes

    If JuMP is not in DIRECT mode, the type returned by backend may change between any JuMP releases. Therefore, only use the public API exposed by MathOptInterface, and do not access internal fields. If you require access to the innermost optimizer, see unsafe_backend. Alternatively, use direct_model to create a JuMP model in DIRECT mode.

    See also: unsafe_backend.

    Example

    julia> import HiGHS
+"_[1]"
    source

    backend

    JuMP.backend — Function
    backend(model::GenericModel)

    Return the lower-level MathOptInterface model that sits underneath JuMP. This model depends on which operating mode JuMP is in (see mode).

    • If JuMP is in DIRECT mode (that is, the model was created using direct_model), the backend will be the optimizer passed to direct_model.
    • If JuMP is in MANUAL or AUTOMATIC mode, the backend is a MOI.Utilities.CachingOptimizer.

    Use index to get the index of a variable or constraint in the backend model.

    Warning

    This function should only be used by advanced users looking to access low-level MathOptInterface or solver-specific functionality.

    Notes

    If JuMP is not in DIRECT mode, the type returned by backend may change between any JuMP releases. Therefore, only use the public API exposed by MathOptInterface, and do not access internal fields. If you require access to the innermost optimizer, see unsafe_backend. Alternatively, use direct_model to create a JuMP model in DIRECT mode.

    See also: unsafe_backend.

    Example

    julia> import HiGHS
 
 julia> model = direct_model(HiGHS.Optimizer());
 
@@ -402,7 +402,7 @@
 A HiGHS model with 1 columns and 0 rows.
 
 julia> index(x)
-MOI.VariableIndex(1)
    source

    barrier_iterations

    JuMP.barrier_iterations — Function
    barrier_iterations(model::GenericModel)

    If available, returns the cumulative number of barrier iterations during the most-recent optimization (the MOI.BarrierIterations attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
+MOI.VariableIndex(1)
    source

    barrier_iterations

    JuMP.barrier_iterations — Function
    barrier_iterations(model::GenericModel)

    If available, returns the cumulative number of barrier iterations during the most-recent optimization (the MOI.BarrierIterations attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -411,7 +411,7 @@
 julia> optimize!(model)
 
 julia> barrier_iterations(model)
-0
    source

    bridge_constraints

    JuMP.bridge_constraints — Function
    bridge_constraints(model::GenericModel)

    When in direct mode, return false.

    When in manual or automatic mode, return a Bool indicating whether the optimizer is set and unsupported constraints are automatically bridged to equivalent supported constraints when an appropriate transformation is available.

    Example

    julia> import Ipopt
+0
    source

    bridge_constraints

    JuMP.bridge_constraints — Function
    bridge_constraints(model::GenericModel)

    When in direct mode, return false.

    When in manual or automatic mode, return a Bool indicating whether the optimizer is set and unsupported constraints are automatically bridged to equivalent supported constraints when an appropriate transformation is available.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
@@ -421,14 +421,14 @@
 julia> model = Model(Ipopt.Optimizer; add_bridges = false);
 
 julia> bridge_constraints(model)
-false
    source

    build_constraint

    JuMP.build_constraint — Function
    build_constraint(error_fn::Function, func, set, args...; kwargs...)

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    build_variable

    build_constraint

    JuMP.build_constraint — Function
    build_constraint(error_fn::Function, func, set, args...; kwargs...)

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    build_variable

    JuMP.build_variable — Function
    build_variable(
     error_fn::Function,
     info::VariableInfo,
     args...;
     kwargs...,
 )

    Return a new AbstractVariable object.

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    Arguments

    • error_fn: a function to call instead of error. error_fn annotates the error message with additional information for the user.
    • info: an instance of VariableInfo. This has a variety of fields relating to the variable such as info.lower_bound and info.binary.
    • args: optional additional positional arguments for extending the @variable macro.
    • kwargs: optional keyword arguments for extending the @variable macro.

    See also: @variable

    Warning

    Extensions should define a method with ONE positional argument to dispatch the call to a different method. Creating an extension that relies on multiple positional arguments leads to MethodErrors if the user passes the arguments in the wrong order.

    Example

    @variable(model, x, Foo)

    will call

    build_variable(error_fn::Function, info::VariableInfo, ::Type{Foo})

    Passing special-case positional arguments such as Bin, Int, and PSD is okay, along with keyword arguments:

    @variable(model, x, Int, Foo(), mykwarg = true)
 # or
-@variable(model, x, Foo(), Int, mykwarg = true)

    will call

    build_variable(error_fn::Function, info::VariableInfo, ::Foo; mykwarg)

    and info.integer will be true.

    Note that the order of the positional arguments does not matter.

    source

    callback_node_status

    JuMP.callback_node_status — Function
    callback_node_status(cb_data, model::GenericModel)

    Return an MOI.CallbackNodeStatusCode enum, indicating if the current primal solution available from callback_value is integer feasible.

    Example

    julia> import Gurobi
+@variable(model, x, Foo(), Int, mykwarg = true)

    will call

    build_variable(error_fn::Function, info::VariableInfo, ::Foo; mykwarg)

    and info.integer will be true.

    Note that the order of the positional arguments does not matter.

    source

    callback_node_status

    JuMP.callback_node_status — Function
    callback_node_status(cb_data, model::GenericModel)

    Return an MOI.CallbackNodeStatusCode enum, indicating if the current primal solution available from callback_value is integer feasible.

    Example

    julia> import Gurobi
 
 julia> model = Model(Gurobi.Optimizer);
 Set parameter WLSAccessID
@@ -455,7 +455,7 @@
 julia> set_attribute(model, Gurobi.CallbackFunction(), my_callback_function)
 
 julia> optimize!(model)
-Status is: CALLBACK_NODE_STATUS_INTEGER
    source

    callback_value

    JuMP.callback_value — Function
    callback_value(cb_data, x::GenericVariableRef)
+Status is: CALLBACK_NODE_STATUS_INTEGER
    source

    callback_value

    JuMP.callback_value — Function
    callback_value(cb_data, x::GenericVariableRef)
 callback_value(cb_data, x::Union{GenericAffExpr,GenericQuadExpr})

    Return the primal solution of x inside a callback.

    cb_data is the argument to the callback function, and the type is dependent on the solver.

    Use callback_node_status to check whether a solution is available.

    Example

    julia> import Gurobi
 
 julia> model = Model(Gurobi.Optimizer);
@@ -484,7 +484,7 @@
 julia> set_attribute(model, Gurobi.CallbackFunction(), my_callback_function)
 
 julia> optimize!(model)
-Solution is: 10.0
    source

    check_belongs_to_model

    check_belongs_to_model

    JuMP.check_belongs_to_model — Function
    check_belongs_to_model(x::AbstractJuMPScalar, model::AbstractModel)
 check_belongs_to_model(x::AbstractConstraint, model::AbstractModel)

    Throw VariableNotOwned if the owner_model of x is not model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
@@ -496,7 +496,7 @@
 julia> check_belongs_to_model(x, model_2)
 ERROR: VariableNotOwned{VariableRef}(x): the variable x cannot be used in this model because
 it belongs to a different model.
-[...]
    source

    coefficient

    JuMP.coefficient — Function
    coefficient(v1::GenericVariableRef{T}, v2::GenericVariableRef{T}) where {T}

    Return one(T) if v1 == v2 and zero(T) otherwise.

    This is a fallback for other coefficient methods to simplify code in which the expression may be a single variable.

    Example

    julia> model = Model();
+[...]
    source

    coefficient

    JuMP.coefficient — Function
    coefficient(v1::GenericVariableRef{T}, v2::GenericVariableRef{T}) where {T}

    Return one(T) if v1 == v2 and zero(T) otherwise.

    This is a fallback for other coefficient methods to simplify code in which the expression may be a single variable.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -504,14 +504,14 @@
 1.0
 
 julia> coefficient(x[1], x[2])
-0.0
    source
    coefficient(a::GenericAffExpr{C,V}, v::V) where {C,V}

    Return the coefficient associated with variable v in the affine expression a.

    Example

    julia> model = Model();
+0.0
    source
    coefficient(a::GenericAffExpr{C,V}, v::V) where {C,V}

    Return the coefficient associated with variable v in the affine expression a.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> expr = 2.0 * x + 1.0;
 
 julia> coefficient(expr, x)
-2.0
    source
    coefficient(a::GenericQuadExpr{C,V}, v1::V, v2::V) where {C,V}

    Return the coefficient associated with the term v1 * v2 in the quadratic expression a.

    Note that coefficient(a, v1, v2) is the same as coefficient(a, v2, v1).

    Example

    julia> model = Model();
+2.0
    source
    coefficient(a::GenericQuadExpr{C,V}, v1::V, v2::V) where {C,V}

    Return the coefficient associated with the term v1 * v2 in the quadratic expression a.

    Note that coefficient(a, v1, v2) is the same as coefficient(a, v2, v1).

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -524,14 +524,14 @@
 2.0
 
 julia> coefficient(expr, x[1], x[1])
-0.0
    source
    coefficient(a::GenericQuadExpr{C,V}, v::V) where {C,V}

    Return the coefficient associated with variable v in the affine component of a.

    Example

    julia> model = Model();
+0.0
    source
    coefficient(a::GenericQuadExpr{C,V}, v::V) where {C,V}

    Return the coefficient associated with variable v in the affine component of a.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> expr = 2.0 * x^2 + 3.0 * x;
 
 julia> coefficient(expr, x)
-3.0
    source

    compute_conflict!

    JuMP.compute_conflict! — Function
    compute_conflict!(model::GenericModel)

    Compute a conflict if the model is infeasible.

    The conflict is also called the Irreducible Infeasible Subsystem (IIS).

    If an optimizer has not been set yet (see set_optimizer), a NoOptimizer error is thrown.

    The status of the conflict can be checked with the MOI.ConflictStatus model attribute. Then, the status for each constraint can be queried with the MOI.ConstraintConflictStatus attribute.

    See also: copy_conflict

    Example

    julia> using JuMP
+3.0
    source

    compute_conflict!

    JuMP.compute_conflict! — Function
    compute_conflict!(model::GenericModel)

    Compute a conflict if the model is infeasible.

    The conflict is also called the Irreducible Infeasible Subsystem (IIS).

    If an optimizer has not been set yet (see set_optimizer), a NoOptimizer error is thrown.

    The status of the conflict can be checked with the MOI.ConflictStatus model attribute. Then, the status for each constraint can be queried with the MOI.ConstraintConflictStatus attribute.

    See also: copy_conflict

    Example

    julia> using JuMP
 
 julia> model = Model(Gurobi.Optimizer);
 
@@ -548,21 +548,21 @@
 julia> compute_conflict!(model)
 
 julia> get_attribute(model, MOI.ConflictStatus())
-CONFLICT_FOUND::ConflictStatusCode = 3
    source

    constant

    JuMP.constant — Function
    constant(aff::GenericAffExpr{C,V})::C

    Return the constant of the affine expression.

    Example

    julia> model = Model();
+CONFLICT_FOUND::ConflictStatusCode = 3
    source

    constant

    JuMP.constant — Function
    constant(aff::GenericAffExpr{C,V})::C

    Return the constant of the affine expression.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> aff = 2.0 * x + 3.0;
 
 julia> constant(aff)
-3.0
    source
    constant(quad::GenericQuadExpr{C,V})::C

    Return the constant of the quadratic expression.

    Example

    julia> model = Model();
+3.0
    source
    constant(quad::GenericQuadExpr{C,V})::C

    Return the constant of the quadratic expression.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> quad = 2.0 * x^2 + 3.0;
 
 julia> constant(quad)
-3.0
    source

    constraint_by_name

    JuMP.constraint_by_name — Function
    constraint_by_name(model::AbstractModel, name::String, [F, S])::Union{ConstraintRef,Nothing}

    Return the reference of the constraint with name attribute name or Nothing if no constraint has this name attribute.

    Throws an error if several constraints have name as their name attribute.

    If F and S are provided, this method addititionally throws an error if the constraint is not an F-in-S contraint where F is either the JuMP or MOI type of the function and S is the MOI type of the set.

    Providing F and S is recommended if you know the type of the function and set since its returned type can be inferred while for the method above (that is, without F and S), the exact return type of the constraint index cannot be inferred.

    Example

    julia> model = Model();
+3.0
    source

    constraint_by_name

    JuMP.constraint_by_name — Function
    constraint_by_name(model::AbstractModel, name::String, [F, S])::Union{ConstraintRef,Nothing}

    Return the reference of the constraint with name attribute name or Nothing if no constraint has this name attribute.

    Throws an error if several constraints have name as their name attribute.

    If F and S are provided, this method addititionally throws an error if the constraint is not an F-in-S contraint where F is either the JuMP or MOI type of the function and S is the MOI type of the set.

    Providing F and S is recommended if you know the type of the function and set since its returned type can be inferred while for the method above (that is, without F and S), the exact return type of the constraint index cannot be inferred.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -578,7 +578,7 @@
 julia> constraint_by_name(model, "con", AffExpr, MOI.EqualTo{Float64})
 
 julia> constraint_by_name(model, "con", QuadExpr, MOI.EqualTo{Float64})
-con : x² = 1
    source

    constraint_object

    JuMP.constraint_object — Function
    constraint_object(con_ref::ConstraintRef)

    Return the underlying constraint data for the constraint referenced by con_ref.

    Example

    A scalar constraint:

    julia> model = Model();
+con : x² = 1
    source

    constraint_object

    JuMP.constraint_object — Function
    constraint_object(con_ref::ConstraintRef)

    Return the underlying constraint data for the constraint referenced by con_ref.

    Example

    A scalar constraint:

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -615,7 +615,7 @@
  x[3]
 
 julia> object.set
-MathOptInterface.SecondOrderCone(3)
    source

    constraint_ref_with_index

    JuMP.constraint_ref_with_index — Function
    constraint_ref_with_index(model::AbstractModel, index::MOI.ConstraintIndex)

    Return a ConstraintRef of model corresponding to index.

    This function is a helper function used internally by JuMP and some JuMP extensions. It should not need to be called in user-code.

    source

    constraint_string

    constraint_ref_with_index

    JuMP.constraint_ref_with_index — Function
    constraint_ref_with_index(model::AbstractModel, index::MOI.ConstraintIndex)

    Return a ConstraintRef of model corresponding to index.

    This function is a helper function used internally by JuMP and some JuMP extensions. It should not need to be called in user-code.

    source

    constraint_string

    JuMP.constraint_string — Function
    constraint_string(
     mode::MIME,
     ref::ConstraintRef;
     in_math_mode::Bool = false,
@@ -626,7 +626,7 @@
 julia> @constraint(model, c, 2 * x <= 1);
 
 julia> constraint_string(MIME("text/plain"), c)
-"c : 2 x ≤ 1"
    source

    constraints_string

    JuMP.constraints_string — Function
    constraints_string(mode, model::AbstractModel)::Vector{String}

    Return a list of Strings describing each constraint of the model.

    Example

    julia> model = Model();
+"c : 2 x ≤ 1"
    source

    constraints_string

    JuMP.constraints_string — Function
    constraints_string(mode, model::AbstractModel)::Vector{String}

    Return a list of Strings describing each constraint of the model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x >= 0);
 
@@ -635,7 +635,7 @@
 julia> constraints_string(MIME("text/plain"), model)
 2-element Vector{String}:
  "c : 2 x ≤ 1"
- "x ≥ 0"
    source

    copy_conflict

    JuMP.copy_conflict — Function
    copy_conflict(model::GenericModel)

    Return a copy of the current conflict for the model model and a GenericReferenceMap that can be used to obtain the variable and constraint reference of the new model corresponding to a given model's reference.

    This is a convenience function that provides a filtering function for copy_model.

    Note

    Model copy is not supported in DIRECT mode, that is, when a model is constructed using the direct_model constructor instead of the Model constructor. Moreover, independently on whether an optimizer was provided at model construction, the new model will have no optimizer, that is, an optimizer will have to be provided to the new model in the optimize! call.

    Example

    In the following example, a model model is constructed with a variable x and two constraints c1 and c2. This model has no solution, as the two constraints are mutually exclusive. The solver is asked to compute a conflict with compute_conflict!. The parts of model participating in the conflict are then copied into a model iis_model.

    julia> using JuMP
+ "x ≥ 0"
    source

    copy_conflict

    JuMP.copy_conflict — Function
    copy_conflict(model::GenericModel)

    Return a copy of the current conflict for the model model and a GenericReferenceMap that can be used to obtain the variable and constraint reference of the new model corresponding to a given model's reference.

    This is a convenience function that provides a filtering function for copy_model.

    Note

    Model copy is not supported in DIRECT mode, that is, when a model is constructed using the direct_model constructor instead of the Model constructor. Moreover, independently on whether an optimizer was provided at model construction, the new model will have no optimizer, that is, an optimizer will have to be provided to the new model in the optimize! call.

    Example

    In the following example, a model model is constructed with a variable x and two constraints c1 and c2. This model has no solution, as the two constraints are mutually exclusive. The solver is asked to compute a conflict with compute_conflict!. The parts of model participating in the conflict are then copied into a model iis_model.

    julia> using JuMP
 
 julia> import Gurobi
 
@@ -663,7 +663,7 @@
 Feasibility
 Subject to
  c1 : x ≥ 2
- c2 : x ≤ 1
    source

    copy_extension_data

    JuMP.copy_extension_data — Function
    copy_extension_data(data, new_model::AbstractModel, model::AbstractModel)

    Return a copy of the extension data data of the model model to the extension data of the new model new_model.

    A method should be added for any JuMP extension storing data in the ext field.

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    Warning

    Do not engage in type piracy by implementing this method for types of data that you did not define! JuMP extensions should store types that they define in model.ext, rather than regular Julia types.

    source

    copy_model

    JuMP.copy_model — Function
    copy_model(model::GenericModel; filter_constraints::Union{Nothing, Function}=nothing)

    Return a copy of the model model and a GenericReferenceMap that can be used to obtain the variable and constraint reference of the new model corresponding to a given model's reference. A Base.copy(::AbstractModel) method has also been implemented, it is similar to copy_model but does not return the reference map.

    If the filter_constraints argument is given, only the constraints for which this function returns true will be copied. This function is given a constraint reference as argument.

    Note

    Model copy is not supported in DIRECT mode, that is, when a model is constructed using the direct_model constructor instead of the Model constructor. Moreover, independently on whether an optimizer was provided at model construction, the new model will have no optimizer, that is, an optimizer will have to be provided to the new model in the optimize! call.

    Example

    In the following example, a model model is constructed with a variable x and a constraint cref. It is then copied into a model new_model with the new references assigned to x_new and cref_new.

    julia> model = Model();
+ c2 : x ≤ 1
    source

    copy_extension_data

    JuMP.copy_extension_data — Function
    copy_extension_data(data, new_model::AbstractModel, model::AbstractModel)

    Return a copy of the extension data data of the model model to the extension data of the new model new_model.

    A method should be added for any JuMP extension storing data in the ext field.

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    Warning

    Do not engage in type piracy by implementing this method for types of data that you did not define! JuMP extensions should store types that they define in model.ext, rather than regular Julia types.

    source

    copy_model

    JuMP.copy_model — Function
    copy_model(model::GenericModel; filter_constraints::Union{Nothing, Function}=nothing)

    Return a copy of the model model and a GenericReferenceMap that can be used to obtain the variable and constraint reference of the new model corresponding to a given model's reference. A Base.copy(::AbstractModel) method has also been implemented, it is similar to copy_model but does not return the reference map.

    If the filter_constraints argument is given, only the constraints for which this function returns true will be copied. This function is given a constraint reference as argument.

    Note

    Model copy is not supported in DIRECT mode, that is, when a model is constructed using the direct_model constructor instead of the Model constructor. Moreover, independently on whether an optimizer was provided at model construction, the new model will have no optimizer, that is, an optimizer will have to be provided to the new model in the optimize! call.

    Example

    In the following example, a model model is constructed with a variable x and a constraint cref. It is then copied into a model new_model with the new references assigned to x_new and cref_new.

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -677,7 +677,7 @@
 x
 
 julia> cref_new = reference_map[cref]
-cref : x = 2
    source

    delete

    JuMP.delete — Function
    delete(model::GenericModel, con_ref::ConstraintRef)

    Delete the constraint associated with constraint_ref from the model model.

    Note that delete does not unregister the name from the model, so adding a new constraint of the same name will throw an error. Use unregister to unregister the name after deletion.

    Example

    julia> model = Model();
+cref : x = 2
    source

    delete

    JuMP.delete — Function
    delete(model::GenericModel, con_ref::ConstraintRef)

    Delete the constraint associated with constraint_ref from the model model.

    Note that delete does not unregister the name from the model, so adding a new constraint of the same name will throw an error. Use unregister to unregister the name after deletion.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -695,7 +695,7 @@
 julia> model[:c]
 ERROR: KeyError: key :c not found
 Stacktrace:
-[...]
    source
    delete(model::GenericModel, con_refs::Vector{<:ConstraintRef})

    Delete the constraints associated with con_refs from the model model.

    Solvers may implement specialized methods for deleting multiple constraints of the same concrete type. These methods may be more efficient than repeatedly calling the single constraint delete method.

    See also: unregister

    Example

    julia> model = Model();
+[...]
    source
    delete(model::GenericModel, con_refs::Vector{<:ConstraintRef})

    Delete the constraints associated with con_refs from the model model.

    Solvers may implement specialized methods for deleting multiple constraints of the same concrete type. These methods may be more efficient than repeatedly calling the single constraint delete method.

    See also: unregister

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:3]);
 
@@ -716,7 +716,7 @@
 julia> model[:c]
 ERROR: KeyError: key :c not found
 Stacktrace:
-[...]
    source
    delete(model::GenericModel, variable_ref::GenericVariableRef)

    Delete the variable associated with variable_ref from the model model.

    Note that delete does not unregister the name from the model, so adding a new variable of the same name will throw an error. Use unregister to unregister the name after deletion.

    Example

    julia> model = Model();
+[...]
    source
    delete(model::GenericModel, variable_ref::GenericVariableRef)

    Delete the variable associated with variable_ref from the model model.

    Note that delete does not unregister the name from the model, so adding a new variable of the same name will throw an error. Use unregister to unregister the name after deletion.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -732,7 +732,7 @@
 julia> model[:x]
 ERROR: KeyError: key :x not found
 Stacktrace:
-[...]
    source
    delete(model::GenericModel, variable_refs::Vector{<:GenericVariableRef})

    Delete the variables associated with variable_refs from the model model. Solvers may implement methods for deleting multiple variables that are more efficient than repeatedly calling the single variable delete method.

    See also: unregister

    Example

    julia> model = Model();
+[...]
    source
    delete(model::GenericModel, variable_refs::Vector{<:GenericVariableRef})

    Delete the variables associated with variable_refs from the model model. Solvers may implement methods for deleting multiple variables that are more efficient than repeatedly calling the single variable delete method.

    See also: unregister

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -747,7 +747,7 @@
 julia> model[:x]
 ERROR: KeyError: key :x not found
 Stacktrace:
-[...]
    source

    delete_lower_bound

    delete_lower_bound

    delete_upper_bound

    delete_upper_bound

    direct_generic_model

    direct_generic_model

    JuMP.direct_generic_model — Function
    direct_generic_model(
     value_type::Type{T},
     backend::MOI.ModelLike;
-) where {T<:Real}

    Return a new JuMP model using backend to store the model and solve it.

    As opposed to the Model constructor, no cache of the model is stored outside of backend and no bridges are automatically applied to backend.

    Notes

    The absence of a cache reduces the memory footprint but, it is important to bear in mind the following implications of creating models using this direct mode:

    • When backend does not support an operation, such as modifying constraints or adding variables/constraints after solving, an error is thrown. For models created using the Model constructor, such situations can be dealt with by storing the modifications in a cache and loading them into the optimizer when optimize! is called.
    • No constraint bridging is supported by default.
    • The optimizer used cannot be changed the model is constructed.
    • The model created cannot be copied.
    source
    direct_generic_model(::Type{T}, factory::MOI.OptimizerWithAttributes)

    Create a direct_generic_model using factory, a MOI.OptimizerWithAttributes object created by optimizer_with_attributes.

    Example

    julia> import HiGHS
+) where {T<:Real}

    Return a new JuMP model using backend to store the model and solve it.

    As opposed to the Model constructor, no cache of the model is stored outside of backend and no bridges are automatically applied to backend.

    Notes

    The absence of a cache reduces the memory footprint but, it is important to bear in mind the following implications of creating models using this direct mode:

    • When backend does not support an operation, such as modifying constraints or adding variables/constraints after solving, an error is thrown. For models created using the Model constructor, such situations can be dealt with by storing the modifications in a cache and loading them into the optimizer when optimize! is called.
    • No constraint bridging is supported by default.
    • The optimizer used cannot be changed the model is constructed.
    • The model created cannot be copied.
    source
    direct_generic_model(::Type{T}, factory::MOI.OptimizerWithAttributes)

    Create a direct_generic_model using factory, a MOI.OptimizerWithAttributes object created by optimizer_with_attributes.

    Example

    julia> import HiGHS
 
 julia> optimizer = optimizer_with_attributes(
            HiGHS.Optimizer,
@@ -798,7 +798,7 @@
 
 julia> set_attribute(model, "presolve", "off")
 
-julia> set_attribute(model, MOI.Silent(), true)
    source

    direct_model

    JuMP.direct_model — Function
    direct_model(backend::MOI.ModelLike)

    Return a new JuMP model using backend to store the model and solve it.

    As opposed to the Model constructor, no cache of the model is stored outside of backend and no bridges are automatically applied to backend.

    Notes

    The absence of a cache reduces the memory footprint but, it is important to bear in mind the following implications of creating models using this direct mode:

    • When backend does not support an operation, such as modifying constraints or adding variables/constraints after solving, an error is thrown. For models created using the Model constructor, such situations can be dealt with by storing the modifications in a cache and loading them into the optimizer when optimize! is called.
    • No constraint bridging is supported by default.
    • The optimizer used cannot be changed the model is constructed.
    • The model created cannot be copied.
    source
    direct_model(factory::MOI.OptimizerWithAttributes)

    Create a direct_model using factory, a MOI.OptimizerWithAttributes object created by optimizer_with_attributes.

    Example

    julia> import HiGHS
+julia> set_attribute(model, MOI.Silent(), true)
    source

    direct_model

    JuMP.direct_model — Function
    direct_model(backend::MOI.ModelLike)

    Return a new JuMP model using backend to store the model and solve it.

    As opposed to the Model constructor, no cache of the model is stored outside of backend and no bridges are automatically applied to backend.

    Notes

    The absence of a cache reduces the memory footprint but, it is important to bear in mind the following implications of creating models using this direct mode:

    • When backend does not support an operation, such as modifying constraints or adding variables/constraints after solving, an error is thrown. For models created using the Model constructor, such situations can be dealt with by storing the modifications in a cache and loading them into the optimizer when optimize! is called.
    • No constraint bridging is supported by default.
    • The optimizer used cannot be changed the model is constructed.
    • The model created cannot be copied.
    source
    direct_model(factory::MOI.OptimizerWithAttributes)

    Create a direct_model using factory, a MOI.OptimizerWithAttributes object created by optimizer_with_attributes.

    Example

    julia> import HiGHS
 
 julia> optimizer = optimizer_with_attributes(
            HiGHS.Optimizer,
@@ -826,7 +826,7 @@
 
 julia> set_attribute(model, "presolve", "off")
 
-julia> set_attribute(model, MOI.Silent(), true)
    source

    drop_zeros!

    JuMP.drop_zeros! — Function
    drop_zeros!(expr::GenericAffExpr)

    Remove terms in the affine expression with 0 coefficients.

    Example

    julia> model = Model();
+julia> set_attribute(model, MOI.Silent(), true)
    source

    drop_zeros!

    JuMP.drop_zeros! — Function
    drop_zeros!(expr::GenericAffExpr)

    Remove terms in the affine expression with 0 coefficients.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -838,7 +838,7 @@
 julia> drop_zeros!(expr)
 
 julia> expr
-x[2]
    source
    drop_zeros!(expr::GenericQuadExpr)

    Remove terms in the quadratic expression with 0 coefficients.

    Example

    julia> model = Model();
+x[2]
    source
    drop_zeros!(expr::GenericQuadExpr)

    Remove terms in the quadratic expression with 0 coefficients.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -850,7 +850,7 @@
 julia> drop_zeros!(expr)
 
 julia> expr
-x[2]²
    source

    dual

    JuMP.dual — Function
    dual(con_ref::ConstraintRef; result::Int = 1)

    Return the dual value of constraint con_ref associated with result index result of the most-recent solution returned by the solver.

    Use has_duals to check if a result exists before asking for values.

    See also: result_count, shadow_price.

    Example

    julia> import HiGHS
+x[2]²
    source

    dual

    JuMP.dual — Function
    dual(con_ref::ConstraintRef; result::Int = 1)

    Return the dual value of constraint con_ref associated with result index result of the most-recent solution returned by the solver.

    Use has_duals to check if a result exists before asking for values.

    See also: result_count, shadow_price.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -869,7 +869,7 @@
 true
 
 julia> dual(c)
--2.0
    source

    dual_objective_value

    JuMP.dual_objective_value — Function
    dual_objective_value(model::GenericModel; result::Int = 1)

    Return the value of the objective of the dual problem associated with result index result of the most-recent solution returned by the solver.

    Throws MOI.UnsupportedAttribute{MOI.DualObjectiveValue} if the solver does not support this attribute.

    This function is equivalent to querying the MOI.DualObjectiveValue attribute.

    See also: result_count.

    Example

    julia> import HiGHS
+-2.0
    source

    dual_objective_value

    JuMP.dual_objective_value — Function
    dual_objective_value(model::GenericModel; result::Int = 1)

    Return the value of the objective of the dual problem associated with result index result of the most-recent solution returned by the solver.

    Throws MOI.UnsupportedAttribute{MOI.DualObjectiveValue} if the solver does not support this attribute.

    This function is equivalent to querying the MOI.DualObjectiveValue attribute.

    See also: result_count.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -887,7 +887,7 @@
 julia> dual_objective_value(model; result = 2)
 ERROR: Result index of attribute MathOptInterface.DualObjectiveValue(2) out of bounds. There are currently 1 solution(s) in the model.
 Stacktrace:
-[...]
    source

    dual_shape

    JuMP.dual_shape — Function
    dual_shape(shape::AbstractShape)::AbstractShape

    Returns the shape of the dual space of the space of objects of shape shape. By default, the dual_shape of a shape is itself. See the examples section below for an example for which this is not the case.

    Example

    Consider polynomial constraints for which the dual is moment constraints and moment constraints for which the dual is polynomial constraints. Shapes for polynomials can be defined as follows:

    struct Polynomial
+[...]
    source

    dual_shape

    JuMP.dual_shape — Function
    dual_shape(shape::AbstractShape)::AbstractShape

    Returns the shape of the dual space of the space of objects of shape shape. By default, the dual_shape of a shape is itself. See the examples section below for an example for which this is not the case.

    Example

    Consider polynomial constraints for which the dual is moment constraints and moment constraints for which the dual is polynomial constraints. Shapes for polynomials can be defined as follows:

    struct Polynomial
     coefficients::Vector{Float64}
     monomials::Vector{Monomial}
 end
@@ -902,7 +902,7 @@
     monomials::Vector{Monomial}
 end
 JuMP.reshape_vector(x::Vector, shape::MomentsShape) = Moments(x, shape.monomials)

    Then dual_shape allows the definition of the shape of the dual of polynomial and moment constraints:

    dual_shape(shape::PolynomialShape) = MomentsShape(shape.monomials)
-dual_shape(shape::MomentsShape) = PolynomialShape(shape.monomials)
    source

    dual_start_value

    JuMP.dual_start_value — Function
    dual_start_value(con_ref::ConstraintRef)

    Return the dual start value (MOI attribute ConstraintDualStart) of the constraint con_ref.

    If no dual start value has been set, dual_start_value will return nothing.

    See also set_dual_start_value.

    Example

    julia> model = Model();
+dual_shape(shape::MomentsShape) = PolynomialShape(shape.monomials)
    source

    dual_start_value

    JuMP.dual_start_value — Function
    dual_start_value(con_ref::ConstraintRef)

    Return the dual start value (MOI attribute ConstraintDualStart) of the constraint con_ref.

    If no dual start value has been set, dual_start_value will return nothing.

    See also set_dual_start_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, start = 2.0);
 
@@ -917,19 +917,19 @@
 
 julia> set_dual_start_value(c, nothing)
 
-julia> dual_start_value(c)
    source

    dual_status

    JuMP.dual_status — Function
    dual_status(model::GenericModel; result::Int = 1)

    Return a MOI.ResultStatusCode describing the status of the most recent dual solution of the solver (that is, the MOI.DualStatus attribute) associated with the result index result.

    See also: result_count.

    Example

    julia> import Ipopt
+julia> dual_start_value(c)
    source

    dual_status

    JuMP.dual_status — Function
    dual_status(model::GenericModel; result::Int = 1)

    Return a MOI.ResultStatusCode describing the status of the most recent dual solution of the solver (that is, the MOI.DualStatus attribute) associated with the result index result.

    See also: result_count.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
 julia> dual_status(model; result = 2)
-NO_SOLUTION::ResultStatusCode = 0
    source

    error_if_direct_mode

    JuMP.error_if_direct_mode — Function
    error_if_direct_mode(model::GenericModel, func::Symbol)

    Errors if model is in direct mode during a call from the function named func.

    Used internally within JuMP, or by JuMP extensions who do not want to support models in direct mode.

    Example

    julia> import HiGHS
+NO_SOLUTION::ResultStatusCode = 0
    source

    error_if_direct_mode

    JuMP.error_if_direct_mode — Function
    error_if_direct_mode(model::GenericModel, func::Symbol)

    Errors if model is in direct mode during a call from the function named func.

    Used internally within JuMP, or by JuMP extensions who do not want to support models in direct mode.

    Example

    julia> import HiGHS
 
 julia> model = direct_model(HiGHS.Optimizer());
 
 julia> error_if_direct_mode(model, :foo)
 ERROR: The `foo` function is not supported in DIRECT mode.
 Stacktrace:
-[...]
    source

    fix

    JuMP.fix — Function
    fix(v::GenericVariableRef, value::Number; force::Bool = false)

    Fix a variable to a value. Update the fixing constraint if one exists, otherwise create a new one.

    If the variable already has variable bounds and force=false, calling fix will throw an error. If force=true, existing variable bounds will be deleted, and the fixing constraint will be added. Note a variable will have no bounds after a call to unfix.

    See also FixRef, is_fixed, fix_value, unfix.

    Example

    julia> model = Model();
+[...]
    source

    fix

    JuMP.fix — Function
    fix(v::GenericVariableRef, value::Number; force::Bool = false)

    Fix a variable to a value. Update the fixing constraint if one exists, otherwise create a new one.

    If the variable already has variable bounds and force=false, calling fix will throw an error. If force=true, existing variable bounds will be deleted, and the fixing constraint will be added. Note a variable will have no bounds after a call to unfix.

    See also FixRef, is_fixed, fix_value, unfix.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -949,7 +949,7 @@
 julia> fix(x, 1.0; force = true)
 
 julia> is_fixed(x)
-true
    source

    fix_discrete_variables

    JuMP.fix_discrete_variables — Function
    fix_discrete_variables([var_value::Function = value,] model::GenericModel)

    Modifies model to convert all binary and integer variables to continuous variables with fixed bounds of var_value(x).

    Return

    Returns a function that can be called without any arguments to restore the original model. The behavior of this function is undefined if additional changes are made to the affected variables in the meantime.

    Notes

    • An error is thrown if semi-continuous or semi-integer constraints are present (support may be added for these in the future).
    • All other constraints are ignored (left in place). This includes discrete constraints like SOS and indicator constraints.

    Example

    julia> model = Model();
+true
    source

    fix_discrete_variables

    JuMP.fix_discrete_variables — Function
    fix_discrete_variables([var_value::Function = value,] model::GenericModel)

    Modifies model to convert all binary and integer variables to continuous variables with fixed bounds of var_value(x).

    Return

    Returns a function that can be called without any arguments to restore the original model. The behavior of this function is undefined if additional changes are made to the affected variables in the meantime.

    Notes

    • An error is thrown if semi-continuous or semi-integer constraints are present (support may be added for these in the future).
    • All other constraints are ignored (left in place). This includes discrete constraints like SOS and indicator constraints.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, Bin, start = 1);
 
@@ -973,12 +973,12 @@
  y ≥ 1
  y ≤ 10
  y integer
- x binary
    source

    fix_value

    JuMP.fix_value — Function
    fix_value(v::GenericVariableRef)

    Return the value to which a variable is fixed.

    Error if one does not exist.

    See also FixRef, is_fixed, fix, unfix.

    Example

    julia> model = Model();
+ x binary
    source

    fix_value

    JuMP.fix_value — Function
    fix_value(v::GenericVariableRef)

    Return the value to which a variable is fixed.

    Error if one does not exist.

    See also FixRef, is_fixed, fix, unfix.

    Example

    julia> model = Model();
 
 julia> @variable(model, x == 1);
 
 julia> fix_value(x)
-1.0
    source

    flatten!

    JuMP.flatten! — Function
    flatten!(expr::GenericNonlinearExpr)

    Flatten a nonlinear expression in-place by lifting nested + and * nodes into a single n-ary operation.

    Motivation

    Nonlinear expressions created using operator overloading can be deeply nested and unbalanced. For example, prod(x for i in 1:4) creates *(x, *(x, *(x, x))) instead of the more preferable *(x, x, x, x).

    Example

    julia> model = Model();
+1.0
    source

    flatten!

    JuMP.flatten! — Function
    flatten!(expr::GenericNonlinearExpr)

    Flatten a nonlinear expression in-place by lifting nested + and * nodes into a single n-ary operation.

    Motivation

    Nonlinear expressions created using operator overloading can be deeply nested and unbalanced. For example, prod(x for i in 1:4) creates *(x, *(x, *(x, x))) instead of the more preferable *(x, x, x, x).

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -990,7 +990,7 @@
 (x²) * x * x
 
 julia> flatten!(sin(prod(x for i in 1:4)))
-sin((x²) * x * x)
    source

    function_string

    function_string

    JuMP.function_string — Function
    function_string(
     mode::MIME,
     func::Union{JuMP.AbstractJuMPScalar,Vector{<:JuMP.AbstractJuMPScalar}},
 )

    Return a String representing the function func using print mode mode.

    Example

    julia> model = Model();
@@ -998,7 +998,7 @@
 julia> @variable(model, x);
 
 julia> function_string(MIME("text/plain"), 2 * x + 1)
-"2 x + 1"
    source

    get_attribute

    get_attribute

    JuMP.get_attribute — Function
    get_attribute(model::GenericModel, attr::MOI.AbstractModelAttribute)
 get_attribute(x::GenericVariableRef, attr::MOI.AbstractVariableAttribute)
 get_attribute(cr::ConstraintRef, attr::MOI.AbstractConstraintAttribute)

    Get the value of a solver-specifc attribute attr.

    This is equivalent to calling MOI.get with the associated MOI model and, for variables and constraints, with the associated MOI.VariableIndex or MOI.ConstraintIndex.

    Example

    julia> model = Model();
 
@@ -1015,7 +1015,7 @@
 "x"
 
 julia> get_attribute(c, MOI.ConstraintName())
-"c"
    source
    get_attribute(
+"c"
    source
    get_attribute(
     model::Union{GenericModel,MOI.OptimizerWithAttributes},
     attr::Union{AbstractString,MOI.AbstractOptimizerAttribute},
 )

    Get the value of a solver-specifc attribute attr.

    This is equivalent to calling MOI.get with the associated MOI model.

    If attr is an AbstractString, it is converted to MOI.RawOptimizerAttribute.

    Example

    julia> import HiGHS
@@ -1034,7 +1034,7 @@
 true
 
 julia> get_attribute(opt, MOI.RawOptimizerAttribute("output_flag"))
-true
    source

    has_duals

    JuMP.has_duals — Function
    has_duals(model::GenericModel; result::Int = 1)

    Return true if the solver has a dual solution in result index result available to query, otherwise return false.

    See also dual, shadow_price, and result_count.

    Example

    julia> import HiGHS
+true
    source

    has_duals

    JuMP.has_duals — Function
    has_duals(model::GenericModel; result::Int = 1)

    Return true if the solver has a dual solution in result index result available to query, otherwise return false.

    See also dual, shadow_price, and result_count.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1053,12 +1053,12 @@
 julia> optimize!(model)
 
 julia> has_duals(model)
-true
    source

    has_lower_bound

    has_lower_bound

    has_start_value

    has_start_value

    JuMP.has_start_value — Function
    has_start_value(variable::AbstractVariableRef)

    Return true if the variable has a start value set, otherwise return false.

    See also: start_value, set_start_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, start = 1.5);
 
@@ -1079,12 +1079,12 @@
 true
 
 julia> start_value(y)
-2.0
    source

    has_upper_bound

    has_upper_bound

    has_values

    JuMP.has_values — Function
    has_values(model::GenericModel; result::Int = 1)

    Return true if the solver has a primal solution in result index result available to query, otherwise return false.

    See also value and result_count.

    Example

    julia> import HiGHS
+true
    source

    has_values

    JuMP.has_values — Function
    has_values(model::GenericModel; result::Int = 1)

    Return true if the solver has a primal solution in result index result available to query, otherwise return false.

    See also value and result_count.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1103,25 +1103,25 @@
 julia> optimize!(model)
 
 julia> has_values(model)
-true
    source

    in_set_string

    JuMP.in_set_string — Function
    in_set_string(mode::MIME, set)

    Return a String representing the membership to the set set using print mode mode.

    Extensions

    JuMP extensions may extend this method for new set types to improve the legibility of their printing.

    Example

    julia> in_set_string(MIME("text/plain"), MOI.Interval(1.0, 2.0))
-"∈ [1, 2]"
    source

    index

    JuMP.index — Function
    index(cr::ConstraintRef)::MOI.ConstraintIndex

    Return the index of the constraint that corresponds to cr in the MOI backend.

    Example

    julia> model = Model();
+true
    source

    in_set_string

    JuMP.in_set_string — Function
    in_set_string(mode::MIME, set)

    Return a String representing the membership to the set set using print mode mode.

    Extensions

    JuMP extensions may extend this method for new set types to improve the legibility of their printing.

    Example

    julia> in_set_string(MIME("text/plain"), MOI.Interval(1.0, 2.0))
+"∈ [1, 2]"
    source

    index

    JuMP.index — Function
    index(cr::ConstraintRef)::MOI.ConstraintIndex

    Return the index of the constraint that corresponds to cr in the MOI backend.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> @constraint(model, c, x >= 0);
 
 julia> index(c)
-MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.GreaterThan{Float64}}(1)
    source
    index(v::GenericVariableRef)::MOI.VariableIndex

    Return the index of the variable that corresponds to v in the MOI backend.

    Example

    julia> model = Model();
+MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.GreaterThan{Float64}}(1)
    source
    index(v::GenericVariableRef)::MOI.VariableIndex

    Return the index of the variable that corresponds to v in the MOI backend.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> index(x)
-MOI.VariableIndex(1)
    source

    is_binary

    is_binary

    is_fixed

    is_fixed

    JuMP.is_fixed — Function
    is_fixed(v::GenericVariableRef)

    Return true if v is a fixed variable. If true, the fixed value can be queried with fix_value.

    See also FixRef, fix_value, fix, unfix.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1131,7 +1131,7 @@
 julia> fix(x, 1.0)
 
 julia> is_fixed(x)
-true
    source

    is_integer

    is_integer

    JuMP.is_integer — Function
    is_integer(v::GenericVariableRef)

    Return true if v is constrained to be integer.

    See also IntegerRef, set_integer, unset_integer.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1141,7 +1141,7 @@
 julia> set_integer(x)
 
 julia> is_integer(x)
-true
    source

    is_parameter

    is_parameter

    is_solved_and_feasible

    is_solved_and_feasible

    JuMP.is_solved_and_feasible — Function
    is_solved_and_feasible(
     model::GenericModel;
     allow_local::Bool = true,
     allow_almost::Bool = false,
@@ -1164,7 +1164,7 @@
 julia> model = Model(Ipopt.Optimizer);
 
 julia> is_solved_and_feasible(model)
-false
    source

    is_valid

    JuMP.is_valid — Function
    is_valid(model::GenericModel, con_ref::ConstraintRef{<:AbstractModel})

    Return true if con_ref refers to a valid constraint in model.

    Example

    julia> model = Model();
+false
    source

    is_valid

    JuMP.is_valid — Function
    is_valid(model::GenericModel, con_ref::ConstraintRef{<:AbstractModel})

    Return true if con_ref refers to a valid constraint in model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1176,7 +1176,7 @@
 julia> model_2 = Model();
 
 julia> is_valid(model_2, c)
-false
    source
    is_valid(model::GenericModel, variable_ref::GenericVariableRef)

    Return true if variable refers to a valid variable in model.

    Example

    julia> model = Model();
+false
    source
    is_valid(model::GenericModel, variable_ref::GenericVariableRef)

    Return true if variable refers to a valid variable in model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1186,7 +1186,7 @@
 julia> model_2 = Model();
 
 julia> is_valid(model_2, x)
-false
    source

    isequal_canonical

    isequal_canonical

    JuMP.isequal_canonical — Function
    isequal_canonical(
     x::T,
     y::T
 ) where {T<:AbstractJuMPScalar,AbstractArray{<:AbstractJuMPScalar}}

    Return true if x is equal to y after dropping zeros and disregarding the order.

    This method is mainly useful for testing, because fallbacks like x == y do not account for valid mathematical comparisons like x[1] + 0 x[2] + 1 == x[1] + 1.

    Example

    julia> model = Model();
@@ -1206,7 +1206,7 @@
 false
 
 julia> isequal_canonical(a, b)
-true
    source

    jump_function

    JuMP.jump_function — Function
    jump_function(model::AbstractModel, x::MOI.AbstractFunction)

    Given an MathOptInterface object x, return the JuMP equivalent.

    See also: moi_function.

    Example

    julia> model = Model();
+true
    source

    jump_function

    JuMP.jump_function — Function
    jump_function(model::AbstractModel, x::MOI.AbstractFunction)

    Given an MathOptInterface object x, return the JuMP equivalent.

    See also: moi_function.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1214,10 +1214,10 @@
 1.0 + 2.0 MOI.VariableIndex(1)
 
 julia> jump_function(model, f)
-2 x + 1
    source

    jump_function_type

    JuMP.jump_function_type — Function
    jump_function_type(model::AbstractModel, ::Type{T}) where {T}

    Given an MathOptInterface object type T, return the JuMP equivalent.

    See also: moi_function_type.

    Example

    julia> model = Model();
+2 x + 1
    source

    jump_function_type

    JuMP.jump_function_type — Function
    jump_function_type(model::AbstractModel, ::Type{T}) where {T}

    Given an MathOptInterface object type T, return the JuMP equivalent.

    See also: moi_function_type.

    Example

    julia> model = Model();
 
 julia> jump_function_type(model, MOI.ScalarAffineFunction{Float64})
-AffExpr (alias for GenericAffExpr{Float64, GenericVariableRef{Float64}})
    source

    latex_formulation

    JuMP.latex_formulation — Function
    latex_formulation(model::AbstractModel)

    Wrap model in a type so that it can be pretty-printed as text/latex in a notebook like IJulia, or in Documenter.

    To render the model, end the cell with latex_formulation(model), or call display(latex_formulation(model)) in to force the display of the model from inside a function.

    source

    linear_terms

    JuMP.linear_terms — Function
    linear_terms(aff::GenericAffExpr{C,V})

    Provides an iterator over coefficient-variable tuples (a_i::C, x_i::V) in the linear part of the affine expression.

    source
    linear_terms(quad::GenericQuadExpr{C,V})

    Provides an iterator over tuples (coefficient::C, variable::V) in the linear part of the quadratic expression.

    source

    list_of_constraint_types

    JuMP.list_of_constraint_types — Function
    list_of_constraint_types(model::GenericModel)::Vector{Tuple{Type,Type}}

    Return a list of tuples of the form (F, S) where F is a JuMP function type and S is an MOI set type such that all_constraints(model, F, S) returns a nonempty list.

    Example

    julia> model = Model();
+AffExpr (alias for GenericAffExpr{Float64, GenericVariableRef{Float64}})
    source

    latex_formulation

    JuMP.latex_formulation — Function
    latex_formulation(model::AbstractModel)

    Wrap model in a type so that it can be pretty-printed as text/latex in a notebook like IJulia, or in Documenter.

    To render the model, end the cell with latex_formulation(model), or call display(latex_formulation(model)) in to force the display of the model from inside a function.

    source

    linear_terms

    JuMP.linear_terms — Function
    linear_terms(aff::GenericAffExpr{C,V})

    Provides an iterator over coefficient-variable tuples (a_i::C, x_i::V) in the linear part of the affine expression.

    source
    linear_terms(quad::GenericQuadExpr{C,V})

    Provides an iterator over tuples (coefficient::C, variable::V) in the linear part of the quadratic expression.

    source

    list_of_constraint_types

    JuMP.list_of_constraint_types — Function
    list_of_constraint_types(model::GenericModel)::Vector{Tuple{Type,Type}}

    Return a list of tuples of the form (F, S) where F is a JuMP function type and S is an MOI set type such that all_constraints(model, F, S) returns a nonempty list.

    Example

    julia> model = Model();
 
 julia> @variable(model, x >= 0, Bin);
 
@@ -1227,12 +1227,12 @@
 3-element Vector{Tuple{Type, Type}}:
  (AffExpr, MathOptInterface.LessThan{Float64})
  (VariableRef, MathOptInterface.GreaterThan{Float64})
- (VariableRef, MathOptInterface.ZeroOne)

    Performance considerations

    Iterating over the list of function and set types is a type-unstable operation. Consider using a function barrier. See the Performance tips for extensions section of the documentation for more details.

    source

    lower_bound

    JuMP.lower_bound — Function
    lower_bound(v::GenericVariableRef)

    Return the lower bound of a variable. Error if one does not exist.

    See also LowerBoundRef, has_lower_bound, set_lower_bound, delete_lower_bound.

    Example

    julia> model = Model();
+ (VariableRef, MathOptInterface.ZeroOne)

    Performance considerations

    Iterating over the list of function and set types is a type-unstable operation. Consider using a function barrier. See the Performance tips for extensions section of the documentation for more details.

    source

    lower_bound

    lp_matrix_data

    JuMP.lp_matrix_data — Function
    lp_matrix_data(model::GenericModel{T})

    Given a JuMP model of a linear program, return an LPMatrixData{T} struct storing data for an equivalent linear program in the form:

    \[\begin{aligned} +1.0

    source

    lp_matrix_data

    JuMP.lp_matrix_data — Function
    lp_matrix_data(model::GenericModel{T})

    Given a JuMP model of a linear program, return an LPMatrixData{T} struct storing data for an equivalent linear program in the form:

    \[\begin{aligned} \min & c^\top x + c_0 \\ & b_l \le A x \le b_u \\ & x_l \le x \le x_u @@ -1277,7 +1277,7 @@ 0.0 julia> data.sense -MAX_SENSE::OptimizationSense = 1

    source

    lp_sensitivity_report

    JuMP.lp_sensitivity_report — Function
    lp_sensitivity_report(model::GenericModel{T}; atol::T = Base.rtoldefault(T))::SensitivityReport{T} where {T}

    Given a linear program model with a current optimal basis, return a SensitivityReport object, which maps:

    • Every variable reference to a tuple (d_lo, d_hi)::Tuple{T,T}, explaining how much the objective coefficient of the corresponding variable can change by, such that the original basis remains optimal.
    • Every constraint reference to a tuple (d_lo, d_hi)::Tuple{T,T}, explaining how much the right-hand side of the corresponding constraint can change by, such that the basis remains optimal.

    Both tuples are relative, rather than absolute. So given a objective coefficient of 1.0 and a tuple (-0.5, 0.5), the objective coefficient can range between 1.0 - 0.5 an 1.0 + 0.5.

    atol is the primal/dual optimality tolerance, and should match the tolerance of the solver used to compute the basis.

    Note: interval constraints are NOT supported.

    Example

    julia> import HiGHS
+MAX_SENSE::OptimizationSense = 1
    source

    lp_sensitivity_report

    JuMP.lp_sensitivity_report — Function
    lp_sensitivity_report(model::GenericModel{T}; atol::T = Base.rtoldefault(T))::SensitivityReport{T} where {T}

    Given a linear program model with a current optimal basis, return a SensitivityReport object, which maps:

    • Every variable reference to a tuple (d_lo, d_hi)::Tuple{T,T}, explaining how much the objective coefficient of the corresponding variable can change by, such that the original basis remains optimal.
    • Every constraint reference to a tuple (d_lo, d_hi)::Tuple{T,T}, explaining how much the right-hand side of the corresponding constraint can change by, such that the basis remains optimal.

    Both tuples are relative, rather than absolute. So given a objective coefficient of 1.0 and a tuple (-0.5, 0.5), the objective coefficient can range between 1.0 - 0.5 an 1.0 + 0.5.

    atol is the primal/dual optimality tolerance, and should match the tolerance of the solver used to compute the basis.

    Note: interval constraints are NOT supported.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1309,7 +1309,7 @@
            "The lower bound of `x` can decrease by $dRHS_lo or increase " *
            "by $dRHS_hi."
        )
-The lower bound of `x` can decrease by -Inf or increase by 3.0.
    source

    map_coefficients

    map_coefficients

    JuMP.map_coefficients — Function
    map_coefficients(f::Function, a::GenericAffExpr)

    Apply f to the coefficients and constant term of an GenericAffExpr a and return a new expression.

    See also: map_coefficients_inplace!

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1320,7 +1320,7 @@
 2 x + 2
 
 julia> a
-x + 1
    source
    map_coefficients(f::Function, a::GenericQuadExpr)

    Apply f to the coefficients and constant term of an GenericQuadExpr a and return a new expression.

    See also: map_coefficients_inplace!

    Example

    julia> model = Model();
+x + 1
    source
    map_coefficients(f::Function, a::GenericQuadExpr)

    Apply f to the coefficients and constant term of an GenericQuadExpr a and return a new expression.

    See also: map_coefficients_inplace!

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1331,7 +1331,7 @@
 2 x² + 2 x + 2
 
 julia> a
-x² + x + 1
    source

    map_coefficients_inplace!

    map_coefficients_inplace!

    JuMP.map_coefficients_inplace! — Function
    map_coefficients_inplace!(f::Function, a::GenericAffExpr)

    Apply f to the coefficients and constant term of an GenericAffExpr a and update them in-place.

    See also: map_coefficients

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1342,7 +1342,7 @@
 2 x + 2
 
 julia> a
-2 x + 2
    source
    map_coefficients_inplace!(f::Function, a::GenericQuadExpr)

    Apply f to the coefficients and constant term of an GenericQuadExpr a and update them in-place.

    See also: map_coefficients

    Example

    julia> model = Model();
+2 x + 2
    source
    map_coefficients_inplace!(f::Function, a::GenericQuadExpr)

    Apply f to the coefficients and constant term of an GenericQuadExpr a and update them in-place.

    See also: map_coefficients

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1353,10 +1353,10 @@
 2 x² + 2 x + 2
 
 julia> a
-2 x² + 2 x + 2
    source

    mode

    JuMP.mode — Function
    mode(model::GenericModel)

    Return the ModelMode of model.

    Example

    julia> model = Model();
+2 x² + 2 x + 2
    source

    mode

    JuMP.mode — Function
    mode(model::GenericModel)

    Return the ModelMode of model.

    Example

    julia> model = Model();
 
 julia> mode(model)
-AUTOMATIC::ModelMode = 0
    source

    model_convert

    model_convert

    JuMP.model_convert — Function
    model_convert(
     model::AbstractModel,
     rhs::Union{
         AbstractConstraint,
@@ -1364,14 +1364,14 @@
         AbstractJuMPScalar,
         MOI.AbstractSet,
     },
-)

    Convert the coefficients and constants of functions and sets in the rhs to the coefficient type value_type(typeof(model)).

    Purpose

    Creating and adding a constraint is a two-step process. The first step calls build_constraint, and the result of that is passed to add_constraint.

    However, because build_constraint does not take the model as an argument, the coefficients and constants of the function or set might be different than value_type(typeof(model)).

    Therefore, the result of build_constraint is converted in a call to model_convert before the result is passed to add_constraint.

    source

    model_string

    JuMP.model_string — Function
    model_string(mode::MIME, model::AbstractModel)

    Return a String representation of model given the mode.

    Example

    julia> model = Model();
+)

    Convert the coefficients and constants of functions and sets in the rhs to the coefficient type value_type(typeof(model)).

    Purpose

    Creating and adding a constraint is a two-step process. The first step calls build_constraint, and the result of that is passed to add_constraint.

    However, because build_constraint does not take the model as an argument, the coefficients and constants of the function or set might be different than value_type(typeof(model)).

    Therefore, the result of build_constraint is converted in a call to model_convert before the result is passed to add_constraint.

    source

    model_string

    JuMP.model_string — Function
    model_string(mode::MIME, model::AbstractModel)

    Return a String representation of model given the mode.

    Example

    julia> model = Model();
 
 julia> @variable(model, x >= 0);
 
 julia> print(model_string(MIME("text/plain"), model))
 Feasibility
 Subject to
- x ≥ 0
    source

    moi_function

    moi_function

    JuMP.moi_function — Function
    moi_function(x::AbstractJuMPScalar)
 moi_function(x::AbstractArray{<:AbstractJuMPScalar})

    Given a JuMP object x, return the MathOptInterface equivalent.

    See also: jump_function.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
@@ -1380,8 +1380,8 @@
 2 x + 1
 
 julia> moi_function(f)
-1.0 + 2.0 MOI.VariableIndex(1)
    source

    moi_function_type

    JuMP.moi_function_type — Function
    moi_function_type(::Type{T}) where {T}

    Given a JuMP object type T, return the MathOptInterface equivalent.

    See also: jump_function_type.

    Example

    julia> moi_function_type(AffExpr)
-MathOptInterface.ScalarAffineFunction{Float64}
    source

    moi_set

    JuMP.moi_set — Function
    moi_set(constraint::AbstractConstraint)

    Return the set of the constraint constraint in the function-in-set form as a MathOptInterface.AbstractSet.

    moi_set(s::AbstractVectorSet, dim::Int)

    Returns the MOI set of dimension dim corresponding to the JuMP set s.

    moi_set(s::AbstractScalarSet)

    Returns the MOI set corresponding to the JuMP set s.

    source

    name

    JuMP.name — Function
    name(con_ref::ConstraintRef)

    Get a constraint's name attribute.

    Example

    julia> model = Model();
+1.0 + 2.0 MOI.VariableIndex(1)
    source

    moi_function_type

    JuMP.moi_function_type — Function
    moi_function_type(::Type{T}) where {T}

    Given a JuMP object type T, return the MathOptInterface equivalent.

    See also: jump_function_type.

    Example

    julia> moi_function_type(AffExpr)
+MathOptInterface.ScalarAffineFunction{Float64}
    source

    moi_set

    JuMP.moi_set — Function
    moi_set(constraint::AbstractConstraint)

    Return the set of the constraint constraint in the function-in-set form as a MathOptInterface.AbstractSet.

    moi_set(s::AbstractVectorSet, dim::Int)

    Returns the MOI set of dimension dim corresponding to the JuMP set s.

    moi_set(s::AbstractScalarSet)

    Returns the MOI set corresponding to the JuMP set s.

    source

    name

    JuMP.name — Function
    name(con_ref::ConstraintRef)

    Get a constraint's name attribute.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1389,7 +1389,7 @@
 c : [2 x] ∈ Nonnegatives()
 
 julia> name(c)
-"c"
    source
    name(v::GenericVariableRef)::String

    Get a variable's name attribute.

    Example

    julia> model = Model();
+"c"
    source
    name(v::GenericVariableRef)::String

    Get a variable's name attribute.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2])
 2-element Vector{VariableRef}:
@@ -1397,10 +1397,10 @@
  x[2]
 
 julia> name(x[1])
-"x[1]"
    source
    name(model::AbstractModel)

    Return the MOI.Name attribute of model's backend, or a default if empty.

    Example

    julia> model = Model();
+"x[1]"
    source
    name(model::AbstractModel)

    Return the MOI.Name attribute of model's backend, or a default if empty.

    Example

    julia> model = Model();
 
 julia> name(model)
-"A JuMP Model"
    source

    node_count

    JuMP.node_count — Function
    node_count(model::GenericModel)

    If available, returns the total number of branch-and-bound nodes explored during the most recent optimization in a Mixed Integer Program (the MOI.NodeCount attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
+"A JuMP Model"
    source

    node_count

    JuMP.node_count — Function
    node_count(model::GenericModel)

    If available, returns the total number of branch-and-bound nodes explored during the most recent optimization in a Mixed Integer Program (the MOI.NodeCount attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1409,7 +1409,7 @@
 julia> optimize!(model)
 
 julia> node_count(model)
-0
    source

    normalized_coefficient

    normalized_coefficient

    JuMP.normalized_coefficient — Function
    normalized_coefficient(
     constraint::ConstraintRef,
     variable::GenericVariableRef,
 )

    Return the coefficient associated with variable in constraint after JuMP has normalized the constraint into its standard form.

    See also set_normalized_coefficient.

    Example

    julia> model = Model();
@@ -1429,7 +1429,7 @@
 julia> normalized_coefficient(con_vec, x)
 2-element Vector{Tuple{Int64, Float64}}:
  (1, 1.0)
- (2, 2.0)
    source
    normalized_coefficient(
+ (2, 2.0)
    source
    normalized_coefficient(
     constraint::ConstraintRef,
     variable_1::GenericVariableRef,
     variable_2::GenericVariableRef,
@@ -1454,7 +1454,7 @@
  (1, 1.0)
 
 julia> normalized_coefficient(con_vec, x[1], x[2])
-Tuple{Int64, Float64}[]
    source

    normalized_rhs

    JuMP.normalized_rhs — Function
    normalized_rhs(constraint::ConstraintRef)

    Return the right-hand side term of constraint after JuMP has converted the constraint into its normalized form.

    See also set_normalized_rhs.

    Example

    julia> model = Model();
+Tuple{Int64, Float64}[]
    source

    normalized_rhs

    JuMP.normalized_rhs — Function
    normalized_rhs(constraint::ConstraintRef)

    Return the right-hand side term of constraint after JuMP has converted the constraint into its normalized form.

    See also set_normalized_rhs.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1462,7 +1462,7 @@
 con : 2 x ≤ 1
 
 julia> normalized_rhs(con)
-1.0
    source

    num_constraints

    num_constraints

    JuMP.num_constraints — Function
    num_constraints(model::GenericModel, function_type, set_type)::Int64

    Return the number of constraints currently in the model where the function has type function_type and the set has type set_type.

    See also list_of_constraint_types and all_constraints.

    Example

    julia> model = Model();
 
 julia> @variable(model, x >= 0, Bin);
 
@@ -1481,7 +1481,7 @@
 1
 
 julia> num_constraints(model, AffExpr, MOI.LessThan{Float64})
-2
    source
    num_constraints(model::GenericModel; count_variable_in_set_constraints::Bool)

    Return the number of constraints in model.

    If count_variable_in_set_constraints == true, then VariableRef constraints such as VariableRef-in-Integer are included. To count only the number of structural constraints (for example, the rows in the constraint matrix of a linear program), pass count_variable_in_set_constraints = false.

    Example

    julia> model = Model();
+2
    source
    num_constraints(model::GenericModel; count_variable_in_set_constraints::Bool)

    Return the number of constraints in model.

    If count_variable_in_set_constraints == true, then VariableRef constraints such as VariableRef-in-Integer are included. To count only the number of structural constraints (for example, the rows in the constraint matrix of a linear program), pass count_variable_in_set_constraints = false.

    Example

    julia> model = Model();
 
 julia> @variable(model, x >= 0, Int);
 
@@ -1491,18 +1491,18 @@
 3
 
 julia> num_constraints(model; count_variable_in_set_constraints = false)
-1
    source

    num_variables

    JuMP.num_variables — Function
    num_variables(model::GenericModel)::Int64

    Returns number of variables in model.

    Example

    julia> model = Model();
+1
    source

    num_variables

    JuMP.num_variables — Function
    num_variables(model::GenericModel)::Int64

    Returns number of variables in model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
 julia> num_variables(model)
-2
    source

    object_dictionary

    JuMP.object_dictionary — Function
    object_dictionary(model::GenericModel)

    Return the dictionary that maps the symbol name of a variable, constraint, or expression to the corresponding object.

    Objects are registered to a specific symbol in the macros. For example, @variable(model, x[1:2, 1:2]) registers the array of variables x to the symbol :x.

    This method should be defined for any subtype of AbstractModel.

    See also: unregister.

    Example

    julia> model = Model();
+2
    source

    object_dictionary

    JuMP.object_dictionary — Function
    object_dictionary(model::GenericModel)

    Return the dictionary that maps the symbol name of a variable, constraint, or expression to the corresponding object.

    Objects are registered to a specific symbol in the macros. For example, @variable(model, x[1:2, 1:2]) registers the array of variables x to the symbol :x.

    This method should be defined for any subtype of AbstractModel.

    See also: unregister.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
 julia> object_dictionary(model)
 Dict{Symbol, Any} with 1 entry:
-  :x => VariableRef[x[1], x[2]]
    source

    objective_bound

    JuMP.objective_bound — Function
    objective_bound(model::GenericModel)

    Return the best known bound on the optimal objective value after a call to optimize!(model).

    For scalar-valued objectives, this function returns a Float64. For vector-valued objectives, it returns a Vector{Float64}.

    In the case of a vector-valued objective, this returns the ideal point, that is, the point obtained if each objective was optimized independently.

    This function is equivalent to querying the MOI.ObjectiveBound attribute.

    Example

    julia> import HiGHS
+  :x => VariableRef[x[1], x[2]]
    source

    objective_bound

    JuMP.objective_bound — Function
    objective_bound(model::GenericModel)

    Return the best known bound on the optimal objective value after a call to optimize!(model).

    For scalar-valued objectives, this function returns a Float64. For vector-valued objectives, it returns a Vector{Float64}.

    In the case of a vector-valued objective, this returns the ideal point, that is, the point obtained if each objective was optimized independently.

    This function is equivalent to querying the MOI.ObjectiveBound attribute.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1515,7 +1515,7 @@
 julia> optimize!(model)
 
 julia> objective_bound(model)
-3.0
    source

    objective_function

    objective_function

    JuMP.objective_function — Function
    objective_function(
     model::GenericModel,
     ::Type{F} = objective_function_type(model),
 ) where {F}

    Return an object of type F representing the objective function.

    Errors if the objective is not convertible to type F.

    This function is equivalent to querying the MOI.ObjectiveFunction{F} attribute.

    Example

    julia> model = Model();
@@ -1535,21 +1535,21 @@
 julia> typeof(objective_function(model, QuadExpr))
 QuadExpr (alias for GenericQuadExpr{Float64, GenericVariableRef{Float64}})

    We see with the last two commands that even if the objective function is affine, as it is convertible to a quadratic function, it can be queried as a quadratic function and the result is quadratic.

    However, it is not convertible to a variable:

    julia> objective_function(model, VariableRef)
 ERROR: InexactError: convert(MathOptInterface.VariableIndex, 1.0 + 2.0 MOI.VariableIndex(1))
-[...]
    source

    objective_function_string

    JuMP.objective_function_string — Function
    objective_function_string(mode, model::AbstractModel)::String

    Return a String describing the objective function of the model.

    Example

    julia> model = Model();
+[...]
    source

    objective_function_string

    JuMP.objective_function_string — Function
    objective_function_string(mode, model::AbstractModel)::String

    Return a String describing the objective function of the model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> @objective(model, Min, 2 * x);
 
 julia> objective_function_string(MIME("text/plain"), model)
-"2 x"
    source

    objective_function_type

    objective_function_type

    JuMP.objective_function_type — Function
    objective_function_type(model::GenericModel)::AbstractJuMPScalar

    Return the type of the objective function.

    This function is equivalent to querying the MOI.ObjectiveFunctionType attribute.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> @objective(model, Min, 2 * x + 1);
 
 julia> objective_function_type(model)
-AffExpr (alias for GenericAffExpr{Float64, GenericVariableRef{Float64}})
    source

    objective_sense

    JuMP.objective_sense — Function
    objective_sense(model::GenericModel)::MOI.OptimizationSense

    Return the objective sense.

    This function is equivalent to querying the MOI.ObjectiveSense attribute.

    Example

    julia> model = Model();
+AffExpr (alias for GenericAffExpr{Float64, GenericVariableRef{Float64}})
    source

    objective_sense

    JuMP.objective_sense — Function
    objective_sense(model::GenericModel)::MOI.OptimizationSense

    Return the objective sense.

    This function is equivalent to querying the MOI.ObjectiveSense attribute.

    Example

    julia> model = Model();
 
 julia> objective_sense(model)
 FEASIBILITY_SENSE::OptimizationSense = 2
@@ -1560,7 +1560,7 @@
 x
 
 julia> objective_sense(model)
-MAX_SENSE::OptimizationSense = 1
    source

    objective_value

    JuMP.objective_value — Function
    objective_value(model::GenericModel; result::Int = 1)

    Return the objective value associated with result index result of the most-recent solution returned by the solver.

    For scalar-valued objectives, this function returns a Float64. For vector-valued objectives, it returns a Vector{Float64}.

    This function is equivalent to querying the MOI.ObjectiveValue attribute.

    See also: result_count.

    Example

    julia> import HiGHS
+MAX_SENSE::OptimizationSense = 1
    source

    objective_value

    JuMP.objective_value — Function
    objective_value(model::GenericModel; result::Int = 1)

    Return the objective value associated with result index result of the most-recent solution returned by the solver.

    For scalar-valued objectives, this function returns a Float64. For vector-valued objectives, it returns a Vector{Float64}.

    This function is equivalent to querying the MOI.ObjectiveValue attribute.

    See also: result_count.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1578,7 +1578,7 @@
 julia> objective_value(model; result = 2)
 ERROR: Result index of attribute MathOptInterface.ObjectiveValue(2) out of bounds. There are currently 1 solution(s) in the model.
 Stacktrace:
-[...]
    source

    op_ifelse

    JuMP.op_ifelse — Function
    op_ifelse(a, x, y)

    A function that falls back to ifelse(a, x, y), but when called with a JuMP variables or expression in the first argument, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
+[...]
    source

    op_ifelse

    JuMP.op_ifelse — Function
    op_ifelse(a, x, y)

    A function that falls back to ifelse(a, x, y), but when called with a JuMP variables or expression in the first argument, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1589,14 +1589,14 @@
 ifelse(x, 1.0, 2.0)
 
 julia> op_ifelse(true, x, 2.0)
-x
    source

    op_string

    JuMP.op_string — Function
    op_string(mime::MIME, x::GenericNonlinearExpr, ::Val{op}) where {op}

    Return the string that should be printed for the operator op when function_string is called with mime and x.

    Example

    julia> model = Model();
+x
    source

    op_string

    JuMP.op_string — Function
    op_string(mime::MIME, x::GenericNonlinearExpr, ::Val{op}) where {op}

    Return the string that should be printed for the operator op when function_string is called with mime and x.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2], Bin);
 
 julia> f = @expression(model, x[1] || x[2]);
 
 julia> op_string(MIME("text/plain"), f, Val(:||))
-"||"
    source

    operator_to_set

    JuMP.operator_to_set — Function
    operator_to_set(error_fn::Function, ::Val{sense_symbol})

    Converts a sense symbol to a set set such that @constraint(model, func sense_symbol 0) is equivalent to @constraint(model, func in set) for any func::AbstractJuMPScalar.

    Example

    Once a custom set is defined you can directly create a JuMP constraint with it:

    julia> struct CustomSet{T} <: MOI.AbstractScalarSet
+"||"
    source

    operator_to_set

    JuMP.operator_to_set — Function
    operator_to_set(error_fn::Function, ::Val{sense_symbol})

    Converts a sense symbol to a set set such that @constraint(model, func sense_symbol 0) is equivalent to @constraint(model, func in set) for any func::AbstractJuMPScalar.

    Example

    Once a custom set is defined you can directly create a JuMP constraint with it:

    julia> struct CustomSet{T} <: MOI.AbstractScalarSet
            value::T
        end
 
@@ -1615,8 +1615,8 @@
 julia> MOIU.shift_constant(set::CustomSet, value) = CustomSet(set.value + value)
 
 julia> cref = @constraint(model, x ⊰ 1)
-x ∈ CustomSet{Float64}(1.0)

    Note that the whole function is first moved to the right-hand side, then the sign is transformed into a set with zero constant and finally the constant is moved to the set with MOIU.shift_constant.

    source

    operator_warn

    JuMP.operator_warn — Function
    operator_warn(model::AbstractModel)
-operator_warn(model::GenericModel)

    This function is called on the model whenever two affine expressions are added together without using destructive_add!, and at least one of the two expressions has more than 50 terms.

    For the case of Model, if this function is called more than 20,000 times then a warning is generated once.

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    optimize!

    JuMP.optimize! — Function
    optimize!(
+x ∈ CustomSet{Float64}(1.0)

    Note that the whole function is first moved to the right-hand side, then the sign is transformed into a set with zero constant and finally the constant is moved to the set with MOIU.shift_constant.

    source

    operator_warn

    JuMP.operator_warn — Function
    operator_warn(model::AbstractModel)
+operator_warn(model::GenericModel)

    This function is called on the model whenever two affine expressions are added together without using destructive_add!, and at least one of the two expressions has more than 50 terms.

    For the case of Model, if this function is called more than 20,000 times then a warning is generated once.

    This method should only be implemented by developers creating JuMP extensions. It should never be called by users of JuMP.

    source

    optimize!

    JuMP.optimize! — Function
    optimize!(
     model::GenericModel;
     ignore_optimize_hook = (model.optimize_hook === nothing),
     kwargs...,
@@ -1636,7 +1636,7 @@
 my_optimize_hook (generic function with 1 method)
 
 julia> optimize!(model; foo = 2)
-Hook called with foo = 2
    source

    optimizer_index

    optimizer_index

    JuMP.optimizer_index — Function
    optimizer_index(x::GenericVariableRef)::MOI.VariableIndex
 optimizer_index(x::ConstraintRef{<:GenericModel})::MOI.ConstraintIndex

    Return the variable or constraint index that corresponds to x in the associated model unsafe_backend(owner_model(x)).

    This function should be used with unsafe_backend.

    As a safer alternative, use backend and index. See the docstrings of backend and unsafe_backend for more details.

    Throws

    • Throws NoOptimizer if no optimizer is set.
    • Throws an ErrorException if the optimizer is set but is not attached.
    • Throws an ErrorException if the index is bridged.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
@@ -1652,7 +1652,7 @@
 A HiGHS model with 1 columns and 0 rows.
 
 julia> optimizer_index(x)
-MOI.VariableIndex(1)
    source

    optimizer_with_attributes

    JuMP.optimizer_with_attributes — Function
    optimizer_with_attributes(optimizer_constructor, attrs::Pair...)

    Groups an optimizer constructor with the list of attributes attrs. Note that it is equivalent to MOI.OptimizerWithAttributes.

    When provided to the Model constructor or to set_optimizer, it creates an optimizer by calling optimizer_constructor(), and then sets the attributes using set_attribute.

    See also: set_attribute, get_attribute.

    Note

    The string names of the attributes are specific to each solver. One should consult the solver's documentation to find the attributes of interest.

    Example

    julia> import HiGHS
+MOI.VariableIndex(1)
    source

    optimizer_with_attributes

    JuMP.optimizer_with_attributes — Function
    optimizer_with_attributes(optimizer_constructor, attrs::Pair...)

    Groups an optimizer constructor with the list of attributes attrs. Note that it is equivalent to MOI.OptimizerWithAttributes.

    When provided to the Model constructor or to set_optimizer, it creates an optimizer by calling optimizer_constructor(), and then sets the attributes using set_attribute.

    See also: set_attribute, get_attribute.

    Note

    The string names of the attributes are specific to each solver. One should consult the solver's documentation to find the attributes of interest.

    Example

    julia> import HiGHS
 
 julia> optimizer = optimizer_with_attributes(
            HiGHS.Optimizer, "presolve" => "off", MOI.Silent() => true,
@@ -1664,12 +1664,12 @@
 
 julia> set_attribute(model, "presolve", "off")
 
-julia> set_attribute(model, MOI.Silent(), true)
    source

    owner_model

    JuMP.owner_model — Function
    owner_model(s::AbstractJuMPScalar)

    Return the model owning the scalar s.

    Example

    julia> model = Model();
+julia> set_attribute(model, MOI.Silent(), true)
    source

    owner_model

    JuMP.owner_model — Function
    owner_model(s::AbstractJuMPScalar)

    Return the model owning the scalar s.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> owner_model(x) === model
-true
    source

    parameter_value

    parameter_value

    JuMP.parameter_value — Function
    parameter_value(x::GenericVariableRef)

    Return the value of the parameter x.

    Errors if x is not a parameter.

    See also ParameterRef, is_parameter, set_parameter_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, p in Parameter(2))
 p
@@ -1680,23 +1680,23 @@
 julia> set_parameter_value(p, 2.5)
 
 julia> parameter_value(p)
-2.5
    source

    parse_constraint

    JuMP.parse_constraint — Function
    parse_constraint(error_fn::Function, expr::Expr)

    The entry-point for all constraint-related parsing.

    Arguments

    • The error_fn function is passed everywhere to provide better error messages
    • expr comes from the @constraint macro. There are two possibilities:
      • @constraint(model, expr)
      • @constraint(model, name[args], expr)
      In both cases, expr is the main component of the constraint.

    Supported syntax

    JuMP currently supports the following expr objects:

    • lhs <= rhs
    • lhs == rhs
    • lhs >= rhs
    • l <= body <= u
    • u >= body >= l
    • lhs ⟂ rhs
    • lhs in rhs
    • lhs ∈ rhs
    • z --> {constraint}
    • !z --> {constraint}
    • z <--> {constraint}
    • !z <--> {constraint}
    • z => {constraint}
    • !z => {constraint}

    as well as all broadcasted variants.

    Extensions

    The infrastructure behind parse_constraint is extendable. See parse_constraint_head and parse_constraint_call for details.

    source

    parse_constraint_call

    parse_constraint

    JuMP.parse_constraint — Function
    parse_constraint(error_fn::Function, expr::Expr)

    The entry-point for all constraint-related parsing.

    Arguments

    • The error_fn function is passed everywhere to provide better error messages
    • expr comes from the @constraint macro. There are two possibilities:
      • @constraint(model, expr)
      • @constraint(model, name[args], expr)
      In both cases, expr is the main component of the constraint.

    Supported syntax

    JuMP currently supports the following expr objects:

    • lhs <= rhs
    • lhs == rhs
    • lhs >= rhs
    • l <= body <= u
    • u >= body >= l
    • lhs ⟂ rhs
    • lhs in rhs
    • lhs ∈ rhs
    • z --> {constraint}
    • !z --> {constraint}
    • z <--> {constraint}
    • !z <--> {constraint}
    • z => {constraint}
    • !z => {constraint}

    as well as all broadcasted variants.

    Extensions

    The infrastructure behind parse_constraint is extendable. See parse_constraint_head and parse_constraint_call for details.

    source

    parse_constraint_call

    JuMP.parse_constraint_call — Function
    parse_constraint_call(
     error_fn::Function,
     is_vectorized::Bool,
     ::Val{op},
     args...,
-)

    Implement this method to intercept the parsing of a :call expression with operator op.

    Warning

    Extending the constraint macro at parse time is an advanced operation and has the potential to interfere with existing JuMP syntax. Please discuss with the developer chatroom before publishing any code that implements these methods.

    Arguments

    • error_fn: a function that accepts a String and throws the string as an error, along with some descriptive information of the macro from which it was thrown.
    • is_vectorized: a boolean to indicate if op should be broadcast or not
    • op: the first element of the .args field of the Expr to intercept
    • args...: the .args field of the Expr.

    Returns

    This function must return:

    • parse_code::Expr: an expression containing any setup or rewriting code that needs to be called before build_constraint
    • build_code::Expr: an expression that calls build_constraint( or build_constraint.( depending on is_vectorized.

    See also: parse_constraint_head, build_constraint

    source
    parse_constraint_call(
+)

    Implement this method to intercept the parsing of a :call expression with operator op.

    Warning

    Extending the constraint macro at parse time is an advanced operation and has the potential to interfere with existing JuMP syntax. Please discuss with the developer chatroom before publishing any code that implements these methods.

    Arguments

    • error_fn: a function that accepts a String and throws the string as an error, along with some descriptive information of the macro from which it was thrown.
    • is_vectorized: a boolean to indicate if op should be broadcast or not
    • op: the first element of the .args field of the Expr to intercept
    • args...: the .args field of the Expr.

    Returns

    This function must return:

    • parse_code::Expr: an expression containing any setup or rewriting code that needs to be called before build_constraint
    • build_code::Expr: an expression that calls build_constraint( or build_constraint.( depending on is_vectorized.

    See also: parse_constraint_head, build_constraint

    source
    parse_constraint_call(
     error_fn::Function,
     vectorized::Bool,
     ::Val{op},
     lhs,
     rhs,
-) where {op}

    Fallback handler for binary operators. These might be infix operators like @constraint(model, lhs op rhs), or normal operators like @constraint(model, op(lhs, rhs)).

    In both cases, we rewrite as lhs - rhs in operator_to_set(error_fn, op).

    See operator_to_set for details.

    source

    parse_constraint_head

    JuMP.parse_constraint_head — Function
    parse_constraint_head(error_fn::Function, ::Val{head}, args...)

    Implement this method to intercept the parsing of an expression with head head.

    Warning

    Extending the constraint macro at parse time is an advanced operation and has the potential to interfere with existing JuMP syntax. Please discuss with the developer chatroom before publishing any code that implements these methods.

    Arguments

    • error_fn: a function that accepts a String and throws the string as an error, along with some descriptive information of the macro from which it was thrown.
    • head: the .head field of the Expr to intercept
    • args...: the .args field of the Expr.

    Returns

    This function must return:

    • is_vectorized::Bool: whether the expression represents a broadcasted expression like x .<= 1
    • parse_code::Expr: an expression containing any setup or rewriting code that needs to be called before build_constraint
    • build_code::Expr: an expression that calls build_constraint( or build_constraint.( depending on is_vectorized.

    Existing implementations

    JuMP currently implements:

    • ::Val{:call}, which forwards calls to parse_constraint_call
    • ::Val{:comparison}, which handles the special case of l <= body <= u.

    See also: parse_constraint_call, build_constraint

    source

    parse_one_operator_variable

    JuMP.parse_one_operator_variable — Function
    parse_one_operator_variable(
+) where {op}

    Fallback handler for binary operators. These might be infix operators like @constraint(model, lhs op rhs), or normal operators like @constraint(model, op(lhs, rhs)).

    In both cases, we rewrite as lhs - rhs in operator_to_set(error_fn, op).

    See operator_to_set for details.

    source

    parse_constraint_head

    JuMP.parse_constraint_head — Function
    parse_constraint_head(error_fn::Function, ::Val{head}, args...)

    Implement this method to intercept the parsing of an expression with head head.

    Warning

    Extending the constraint macro at parse time is an advanced operation and has the potential to interfere with existing JuMP syntax. Please discuss with the developer chatroom before publishing any code that implements these methods.

    Arguments

    • error_fn: a function that accepts a String and throws the string as an error, along with some descriptive information of the macro from which it was thrown.
    • head: the .head field of the Expr to intercept
    • args...: the .args field of the Expr.

    Returns

    This function must return:

    • is_vectorized::Bool: whether the expression represents a broadcasted expression like x .<= 1
    • parse_code::Expr: an expression containing any setup or rewriting code that needs to be called before build_constraint
    • build_code::Expr: an expression that calls build_constraint( or build_constraint.( depending on is_vectorized.

    Existing implementations

    JuMP currently implements:

    • ::Val{:call}, which forwards calls to parse_constraint_call
    • ::Val{:comparison}, which handles the special case of l <= body <= u.

    See also: parse_constraint_call, build_constraint

    source

    parse_one_operator_variable

    JuMP.parse_one_operator_variable — Function
    parse_one_operator_variable(
     error_fn::Function,
     info_expr::_VariableInfoExpr,
     sense::Val{S},
     value,
-) where {S}

    Update infoexr for a variable expression in the @variable macro of the form variable name S value.

    source

    parse_ternary_variable

    JuMP.parse_ternary_variable — Function
    parse_ternary_variable(error_fn, info_expr, lhs_sense, lhs, rhs_sense, rhs)

    A hook for JuMP extensions to intercept the parsing of a :comparison expression, which has the form lhs lhs_sense variable rhs_sense rhs.

    source

    parse_variable

    JuMP.parse_variable — Function
    parse_variable(error_fn::Function, ::_VariableInfoExpr, args...)

    A hook for extensions to intercept the parsing of inequality constraints in the @variable macro.

    source

    primal_feasibility_report

    JuMP.primal_feasibility_report — Function
    primal_feasibility_report(
+) where {S}

    Update infoexr for a variable expression in the @variable macro of the form variable name S value.

    source

    parse_ternary_variable

    JuMP.parse_ternary_variable — Function
    parse_ternary_variable(error_fn, info_expr, lhs_sense, lhs, rhs_sense, rhs)

    A hook for JuMP extensions to intercept the parsing of a :comparison expression, which has the form lhs lhs_sense variable rhs_sense rhs.

    source

    parse_variable

    JuMP.parse_variable — Function
    parse_variable(error_fn::Function, ::_VariableInfoExpr, args...)

    A hook for extensions to intercept the parsing of inequality constraints in the @variable macro.

    source

    primal_feasibility_report

    JuMP.primal_feasibility_report — Function
    primal_feasibility_report(
     model::GenericModel{T},
     point::AbstractDict{GenericVariableRef{T},T} = _last_primal_solution(model),
     atol::T = zero(T),
@@ -1707,7 +1707,7 @@
 
 julia> primal_feasibility_report(model, Dict(x => 0.2))
 Dict{Any, Float64} with 1 entry:
-  x ≥ 0.5 => 0.3
    source
    primal_feasibility_report(
+  x ≥ 0.5 => 0.3
    source
    primal_feasibility_report(
     point::Function,
     model::GenericModel{T};
     atol::T = zero(T),
@@ -1720,30 +1720,30 @@
            return start_value(v)
        end
 Dict{Any, Float64} with 1 entry:
-  x ≤ 1 => 0.3
    source

    primal_status

    primal_status

    JuMP.primal_status — Function
    primal_status(model::GenericModel; result::Int = 1)

    Return a MOI.ResultStatusCode describing the status of the most recent primal solution of the solver (that is, the MOI.PrimalStatus attribute) associated with the result index result.

    See also: result_count.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
 julia> primal_status(model; result = 2)
-NO_SOLUTION::ResultStatusCode = 0
    source
    JuMP.print_active_bridges — Function
    print_active_bridges([io::IO = stdout,] model::GenericModel)

    Print a list of the variable, constraint, and objective bridges that are currently used in the model.

    source
    print_active_bridges([io::IO = stdout,] model::GenericModel, ::Type{F}) where {F}

    Print a list of bridges required for an objective function of type F.

    source
    print_active_bridges(
+NO_SOLUTION::ResultStatusCode = 0
    source
    JuMP.print_active_bridges — Function
    print_active_bridges([io::IO = stdout,] model::GenericModel)

    Print a list of the variable, constraint, and objective bridges that are currently used in the model.

    source
    print_active_bridges([io::IO = stdout,] model::GenericModel, ::Type{F}) where {F}

    Print a list of bridges required for an objective function of type F.

    source
    print_active_bridges(
     [io::IO = stdout,]
     model::GenericModel,
     F::Type,
     S::Type{<:MOI.AbstractSet},
-)

    Print a list of bridges required for a constraint of type F-in-S.

    source
    print_active_bridges(
+)

    Print a list of bridges required for a constraint of type F-in-S.

    source
    print_active_bridges(
     [io::IO = stdout,]
     model::GenericModel,
     S::Type{<:MOI.AbstractSet},
-)

    Print a list of bridges required to add a variable constrained to the set S.

    source
    JuMP.print_bridge_graph — Function
     print_bridge_graph([io::IO,] model::GenericModel)

    Print the hyper-graph containing all variable, constraint, and objective types that could be obtained by bridging the variables, constraints, and objectives that are present in the model.

    Warning

    This function is intended for advanced users. If you want to see only the bridges that are currently used, use print_active_bridges instead.

    Explanation of output

    Each node in the hyper-graph corresponds to a variable, constraint, or objective type.

    • Variable nodes are indicated by [ ]
    • Constraint nodes are indicated by ( )
    • Objective nodes are indicated by | |

    The number inside each pair of brackets is an index of the node in the hyper-graph.

    Note that this hyper-graph is the full list of possible transformations. When the bridged model is created, we select the shortest hyper-path(s) from this graph, so many nodes may be un-used.

    For more information, see Legat, B., Dowson, O., Garcia, J., and Lubin, M. (2020). "MathOptInterface: a data structure for mathematical optimization problems." URL: https://arxiv.org/abs/2002.03447

    source

    quad_terms

    JuMP.quad_terms — Function
    quad_terms(quad::GenericQuadExpr{C,V})

    Provides an iterator over tuples (coefficient::C, var_1::V, var_2::V) in the quadratic part of the quadratic expression.

    source

    raw_status

    JuMP.raw_status — Function
    raw_status(model::GenericModel)

    Return the reason why the solver stopped in its own words (that is, the MathOptInterface model attribute MOI.RawStatusString).

    Example

    julia> import Ipopt
+)

    Print a list of bridges required to add a variable constrained to the set S.

    source
    JuMP.print_bridge_graph — Function
     print_bridge_graph([io::IO,] model::GenericModel)

    Print the hyper-graph containing all variable, constraint, and objective types that could be obtained by bridging the variables, constraints, and objectives that are present in the model.

    Warning

    This function is intended for advanced users. If you want to see only the bridges that are currently used, use print_active_bridges instead.

    Explanation of output

    Each node in the hyper-graph corresponds to a variable, constraint, or objective type.

    • Variable nodes are indicated by [ ]
    • Constraint nodes are indicated by ( )
    • Objective nodes are indicated by | |

    The number inside each pair of brackets is an index of the node in the hyper-graph.

    Note that this hyper-graph is the full list of possible transformations. When the bridged model is created, we select the shortest hyper-path(s) from this graph, so many nodes may be un-used.

    For more information, see Legat, B., Dowson, O., Garcia, J., and Lubin, M. (2020). "MathOptInterface: a data structure for mathematical optimization problems." URL: https://arxiv.org/abs/2002.03447

    source

    quad_terms

    JuMP.quad_terms — Function
    quad_terms(quad::GenericQuadExpr{C,V})

    Provides an iterator over tuples (coefficient::C, var_1::V, var_2::V) in the quadratic part of the quadratic expression.

    source

    raw_status

    JuMP.raw_status — Function
    raw_status(model::GenericModel)

    Return the reason why the solver stopped in its own words (that is, the MathOptInterface model attribute MOI.RawStatusString).

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
 julia> raw_status(model)
-"optimize not called"
    source

    read_from_file

    read_from_file

    JuMP.read_from_file — Function
    read_from_file(
     filename::String;
     format::MOI.FileFormats.FileFormat = MOI.FileFormats.FORMAT_AUTOMATIC,
     kwargs...,
-)

    Return a JuMP model read from filename in the format format.

    If the filename ends in .gz, it will be uncompressed using GZip. If the filename ends in .bz2, it will be uncompressed using BZip2.

    Other kwargs are passed to the Model constructor of the chosen format.

    source

    reduced_cost

    JuMP.reduced_cost — Function
    reduced_cost(x::GenericVariableRef{T})::T where {T}

    Return the reduced cost associated with variable x.

    One interpretation of the reduced cost is that it is the change in the objective from an infinitesimal relaxation of the variable bounds.

    This method is equivalent to querying the shadow price of the active variable bound (if one exists and is active).

    See also: shadow_price.

    Example

    julia> import HiGHS
+)

    Return a JuMP model read from filename in the format format.

    If the filename ends in .gz, it will be uncompressed using GZip. If the filename ends in .bz2, it will be uncompressed using BZip2.

    Other kwargs are passed to the Model constructor of the chosen format.

    source

    reduced_cost

    JuMP.reduced_cost — Function
    reduced_cost(x::GenericVariableRef{T})::T where {T}

    Return the reduced cost associated with variable x.

    One interpretation of the reduced cost is that it is the change in the objective from an infinitesimal relaxation of the variable bounds.

    This method is equivalent to querying the shadow price of the active variable bound (if one exists and is active).

    See also: shadow_price.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1759,7 +1759,7 @@
 true
 
 julia> reduced_cost(x)
-2.0
    source

    relative_gap

    JuMP.relative_gap — Function
    relative_gap(model::GenericModel)

    Return the final relative optimality gap after a call to optimize!(model).

    Exact value depends upon implementation of MOI.RelativeGap by the particular solver used for optimization.

    This function is equivalent to querying the MOI.RelativeGap attribute.

    Example

    julia> import HiGHS
+2.0
    source

    relative_gap

    JuMP.relative_gap — Function
    relative_gap(model::GenericModel)

    Return the final relative optimality gap after a call to optimize!(model).

    Exact value depends upon implementation of MOI.RelativeGap by the particular solver used for optimization.

    This function is equivalent to querying the MOI.RelativeGap attribute.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -1772,7 +1772,7 @@
 julia> optimize!(model)
 
 julia> relative_gap(model)
-0.0
    source

    relax_integrality

    JuMP.relax_integrality — Function
    relax_integrality(model::GenericModel)

    Modifies model to "relax" all binary and integrality constraints on variables. Specifically,

    • Binary constraints are deleted, and variable bounds are tightened if necessary to ensure the variable is constrained to the interval $[0, 1]$.
    • Integrality constraints are deleted without modifying variable bounds.
    • An error is thrown if semi-continuous or semi-integer constraints are present (support may be added for these in the future).
    • All other constraints are ignored (left in place). This includes discrete constraints like SOS and indicator constraints.

    Returns a function that can be called without any arguments to restore the original model. The behavior of this function is undefined if additional changes are made to the affected variables in the meantime.

    Example

    julia> model = Model();
+0.0
    source

    relax_integrality

    JuMP.relax_integrality — Function
    relax_integrality(model::GenericModel)

    Modifies model to "relax" all binary and integrality constraints on variables. Specifically,

    • Binary constraints are deleted, and variable bounds are tightened if necessary to ensure the variable is constrained to the interval $[0, 1]$.
    • Integrality constraints are deleted without modifying variable bounds.
    • An error is thrown if semi-continuous or semi-integer constraints are present (support may be added for these in the future).
    • All other constraints are ignored (left in place). This includes discrete constraints like SOS and indicator constraints.

    Returns a function that can be called without any arguments to restore the original model. The behavior of this function is undefined if additional changes are made to the affected variables in the meantime.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, Bin);
 
@@ -1798,7 +1798,7 @@
  y ≥ 1
  y ≤ 10
  y integer
- x binary
    source

    relax_with_penalty!

    relax_with_penalty!

    JuMP.relax_with_penalty! — Function
    relax_with_penalty!(
     model::GenericModel{T},
     [penalties::Dict{ConstraintRef,T}];
     [default::Union{Nothing,Real} = nothing,]
@@ -1841,7 +1841,7 @@
 Subject to
  c2 : 3 x + _[2] ≥ 0
  c1 : 2 x ≤ -1
- _[2] ≥ 0
    source

    remove_bridge

    remove_bridge

    JuMP.remove_bridge — Function
    remove_bridge(
     model::GenericModel{S},
     BT::Type{<:MOI.Bridges.AbstractBridge};
     coefficient_type::Type{T} = S,
@@ -1861,17 +1861,17 @@
            model,
            MOI.Bridges.Constraint.NumberConversionBridge;
            coefficient_type = Complex{Float64},
-       )
    source

    reshape_set

    JuMP.reshape_set — Function
    reshape_set(vectorized_set::MOI.AbstractSet, shape::AbstractShape)

    Return a set in its original shape shape given its vectorized form vectorized_form.

    Example

    Given a SymmetricMatrixShape of vectorized form [1, 2, 3] in MOI.PositiveSemidefinieConeTriangle(2), the following code returns the set of the original constraint Symmetric(Matrix[1 2; 2 3]) in PSDCone():

    julia> reshape_set(MOI.PositiveSemidefiniteConeTriangle(2), SymmetricMatrixShape(2))
-PSDCone()
    source

    reshape_vector

    JuMP.reshape_vector — Function
    reshape_vector(vectorized_form::Vector, shape::AbstractShape)

    Return an object in its original shape shape given its vectorized form vectorized_form.

    Example

    Given a SymmetricMatrixShape of vectorized form [1, 2, 3], the following code returns the matrix Symmetric(Matrix[1 2; 2 3]):

    julia> reshape_vector([1, 2, 3], SymmetricMatrixShape(2))
+       )
    source

    reshape_set

    JuMP.reshape_set — Function
    reshape_set(vectorized_set::MOI.AbstractSet, shape::AbstractShape)

    Return a set in its original shape shape given its vectorized form vectorized_form.

    Example

    Given a SymmetricMatrixShape of vectorized form [1, 2, 3] in MOI.PositiveSemidefinieConeTriangle(2), the following code returns the set of the original constraint Symmetric(Matrix[1 2; 2 3]) in PSDCone():

    julia> reshape_set(MOI.PositiveSemidefiniteConeTriangle(2), SymmetricMatrixShape(2))
+PSDCone()
    source

    reshape_vector

    JuMP.reshape_vector — Function
    reshape_vector(vectorized_form::Vector, shape::AbstractShape)

    Return an object in its original shape shape given its vectorized form vectorized_form.

    Example

    Given a SymmetricMatrixShape of vectorized form [1, 2, 3], the following code returns the matrix Symmetric(Matrix[1 2; 2 3]):

    julia> reshape_vector([1, 2, 3], SymmetricMatrixShape(2))
 2×2 LinearAlgebra.Symmetric{Int64, Matrix{Int64}}:
  1  2
- 2  3
    source

    result_count

    JuMP.result_count — Function
    result_count(model::GenericModel)

    Return the number of results available to query after a call to optimize!.

    Example

    julia> import Ipopt
+ 2  3
    source

    result_count

    JuMP.result_count — Function
    result_count(model::GenericModel)

    Return the number of results available to query after a call to optimize!.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
 julia> result_count(model)
-0
    source

    reverse_sense

    JuMP.reverse_sense — Function
    reverse_sense(::Val{T}) where {T}

    Given an (in)equality symbol T, return a new Val object with the opposite (in)equality symbol.

    This function is intended for use in JuMP extensions.

    Example

    julia> reverse_sense(Val(:>=))
-Val{:<=}()
    source

    set_attribute

    reverse_sense

    JuMP.reverse_sense — Function
    reverse_sense(::Val{T}) where {T}

    Given an (in)equality symbol T, return a new Val object with the opposite (in)equality symbol.

    This function is intended for use in JuMP extensions.

    Example

    julia> reverse_sense(Val(:>=))
+Val{:<=}()
    source

    set_attribute

    JuMP.set_attribute — Function
    set_attribute(model::GenericModel, attr::MOI.AbstractModelAttribute, value)
 set_attribute(x::GenericVariableRef, attr::MOI.AbstractVariableAttribute, value)
 set_attribute(cr::ConstraintRef, attr::MOI.AbstractConstraintAttribute, value)

    Set the value of a solver-specifc attribute attr to value.

    This is equivalent to calling MOI.set with the associated MOI model and, for variables and constraints, with the associated MOI.VariableIndex or MOI.ConstraintIndex.

    Example

    julia> model = Model();
 
@@ -1885,7 +1885,7 @@
 
 julia> set_attribute(x, MOI.VariableName(), "x_new")
 
-julia> set_attribute(c, MOI.ConstraintName(), "c_new")
    source
    set_attribute(
+julia> set_attribute(c, MOI.ConstraintName(), "c_new")
    source
    set_attribute(
     model::Union{GenericModel,MOI.OptimizerWithAttributes},
     attr::Union{AbstractString,MOI.AbstractOptimizerAttribute},
     value,
@@ -1901,7 +1901,7 @@
 
 julia> set_attribute(opt, "output_flag", true)
 
-julia> set_attribute(opt, MOI.RawOptimizerAttribute("output_flag"), false)
    source

    set_attributes

    JuMP.set_attributes — Function
    set_attributes(
+julia> set_attribute(opt, MOI.RawOptimizerAttribute("output_flag"), false)
    source

    set_attributes

    JuMP.set_attributes — Function
    set_attributes(
     destination::Union{
         GenericModel,
         MOI.OptimizerWithAttributes,
@@ -1919,7 +1919,7 @@
 
 julia> set_attribute(model, "tol", 1e-4)
 
-julia> set_attribute(model, "max_iter", 100)
    source

    set_binary

    JuMP.set_binary — Function
    set_binary(v::GenericVariableRef)

    Add a constraint on the variable v that it must take values in the set $\{0,1\}$.

    See also BinaryRef, is_binary, unset_binary.

    Example

    julia> model = Model();
+julia> set_attribute(model, "max_iter", 100)
    source

    set_binary

    JuMP.set_binary — Function
    set_binary(v::GenericVariableRef)

    Add a constraint on the variable v that it must take values in the set $\{0,1\}$.

    See also BinaryRef, is_binary, unset_binary.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1929,7 +1929,7 @@
 julia> set_binary(x)
 
 julia> is_binary(x)
-true
    source

    set_dual_start_value

    JuMP.set_dual_start_value — Function
    set_dual_start_value(con_ref::ConstraintRef, value)

    Set the dual start value (MOI attribute ConstraintDualStart) of the constraint con_ref to value.

    To remove a dual start value set it to nothing.

    See also dual_start_value.

    Example

    julia> model = Model();
+true
    source

    set_dual_start_value

    JuMP.set_dual_start_value — Function
    set_dual_start_value(con_ref::ConstraintRef, value)

    Set the dual start value (MOI attribute ConstraintDualStart) of the constraint con_ref to value.

    To remove a dual start value set it to nothing.

    See also dual_start_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, start = 2.0);
 
@@ -1944,7 +1944,7 @@
 
 julia> set_dual_start_value(c, nothing)
 
-julia> dual_start_value(c)
    source

    set_integer

    set_integer

    JuMP.set_integer — Function
    set_integer(variable_ref::GenericVariableRef)

    Add an integrality constraint on the variable variable_ref.

    See also IntegerRef, is_integer, unset_integer.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1954,7 +1954,7 @@
 julia> set_integer(x)
 
 julia> is_integer(x)
-true
    source

    set_lower_bound

    set_lower_bound

    set_name

    JuMP.set_name — Function
    set_name(con_ref::ConstraintRef, s::AbstractString)

    Set a constraint's name attribute.

    Example

    julia> model = Model();
+2.0
    source

    set_name

    JuMP.set_name — Function
    set_name(con_ref::ConstraintRef, s::AbstractString)

    Set a constraint's name attribute.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -1977,7 +1977,7 @@
 "my_constraint"
 
 julia> c
-my_constraint : [2 x] ∈ Nonnegatives()
    source
    set_name(v::GenericVariableRef, s::AbstractString)

    Set a variable's name attribute.

    Example

    julia> model = Model();
+my_constraint : [2 x] ∈ Nonnegatives()
    source
    set_name(v::GenericVariableRef, s::AbstractString)

    Set a variable's name attribute.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -1988,7 +1988,7 @@
 x_foo
 
 julia> name(x)
-"x_foo"
    source

    set_normalized_coefficient

    set_normalized_coefficient

    JuMP.set_normalized_coefficient — Function
    set_normalized_coefficient(
     constraint::ConstraintRef,
     variable::GenericVariableRef,
     value::Number,
@@ -2003,7 +2003,7 @@
 julia> set_normalized_coefficient(con, x, 4)
 
 julia> con
-con : 4 x ≤ 2
    source
    set_normalized_coefficient(
+con : 4 x ≤ 2
    source
    set_normalized_coefficient(
     constraints::AbstractVector{<:ConstraintRef},
     variables::AbstractVector{<:GenericVariableRef},
     values::AbstractVector{<:Number},
@@ -2021,7 +2021,7 @@
 julia> set_normalized_coefficient([con, con], [x, y], [6, 7])
 
 julia> con
-con : 6 x + 7 y ≤ 2
    source
    set_normalized_coefficient(
+con : 6 x + 7 y ≤ 2
    source
    set_normalized_coefficient(
     con_ref::ConstraintRef,
     variable::AbstractVariableRef,
     new_coefficients::Vector{Tuple{Int64,T}},
@@ -2036,7 +2036,7 @@
 julia> set_normalized_coefficient(con, x, [(1, 2.0), (2, 5.0)])
 
 julia> con
-con : [2 x, 5 x] ∈ MathOptInterface.Nonnegatives(2)
    source
    set_normalized_coefficient(
+con : [2 x, 5 x] ∈ MathOptInterface.Nonnegatives(2)
    source
    set_normalized_coefficient(
     constraint::ConstraintRef,
     variable_1:GenericVariableRef,
     variable_2:GenericVariableRef,
@@ -2053,7 +2053,7 @@
 julia> set_normalized_coefficient(con, x[1], x[2], 5)
 
 julia> con
-con : 4 x[1]² + 5 x[1]*x[2] + x[2] ≤ 2
    source
    set_normalized_coefficient(
+con : 4 x[1]² + 5 x[1]*x[2] + x[2] ≤ 2
    source
    set_normalized_coefficient(
     constraints::AbstractVector{<:ConstraintRef},
     variables_1:AbstractVector{<:GenericVariableRef},
     variables_2:AbstractVector{<:GenericVariableRef},
@@ -2068,7 +2068,7 @@
 julia> set_normalized_coefficient([con, con], [x[1], x[1]], [x[1], x[2]], [4, 5])
 
 julia> con
-con : 4 x[1]² + 5 x[1]*x[2] + x[2] ≤ 2
    source

    set_normalized_rhs

    JuMP.set_normalized_rhs — Function
    set_normalized_rhs(constraint::ConstraintRef, value::Number)

    Set the right-hand side term of constraint to value.

    Note that prior to this step, JuMP will aggregate all constant terms onto the right-hand side of the constraint. For example, given a constraint 2x + 1 <= 2, set_normalized_rhs(con, 4) will create the constraint 2x <= 4, not 2x + 1 <= 4.

    Example

    julia> model = Model();
+con : 4 x[1]² + 5 x[1]*x[2] + x[2] ≤ 2
    source

    set_normalized_rhs

    JuMP.set_normalized_rhs — Function
    set_normalized_rhs(constraint::ConstraintRef, value::Number)

    Set the right-hand side term of constraint to value.

    Note that prior to this step, JuMP will aggregate all constant terms onto the right-hand side of the constraint. For example, given a constraint 2x + 1 <= 2, set_normalized_rhs(con, 4) will create the constraint 2x <= 4, not 2x + 1 <= 4.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -2078,7 +2078,7 @@
 julia> set_normalized_rhs(con, 4)
 
 julia> con
-con : 2 x ≤ 4
    source
    set_normalized_rhs(
+con : 2 x ≤ 4
    source
    set_normalized_rhs(
     constraints::AbstractVector{<:ConstraintRef},
     values::AbstractVector{<:Number}
 )

    Set the right-hand side terms of all constraints to values.

    Note that prior to this step, JuMP will aggregate all constant terms onto the right-hand side of the constraint. For example, given a constraint 2x + 1 <= 2, set_normalized_rhs([con], [4]) will create the constraint 2x <= 4, not 2x + 1 <= 4.

    Example

    julia> model = Model();
@@ -2097,12 +2097,12 @@
 con1 : 2 x ≤ 4
 
 julia> con2
-con2 : 3 x ≤ 5
    source

    set_objective

    set_objective

    JuMP.set_objective — Function
    set_objective(model::AbstractModel, sense::MOI.OptimizationSense, func)

    The functional equivalent of the @objective macro.

    Sets the objective sense and objective function simultaneously, and is equivalent to calling set_objective_sense and set_objective_function separately.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
 
-julia> set_objective(model, MIN_SENSE, x)
    source

    set_objective_coefficient

    set_objective_coefficient

    JuMP.set_objective_coefficient — Function
    set_objective_coefficient(
     model::GenericModel,
     variable::GenericVariableRef,
     coefficient::Real,
@@ -2116,7 +2116,7 @@
 julia> set_objective_coefficient(model, x, 3)
 
 julia> objective_function(model)
-3 x + 1
    source
    set_objective_coefficient(
+3 x + 1
    source
    set_objective_coefficient(
     model::GenericModel,
     variables::Vector{<:GenericVariableRef},
     coefficients::Vector{<:Real},
@@ -2132,7 +2132,7 @@
 julia> set_objective_coefficient(model, [x, y], [5, 4])
 
 julia> objective_function(model)
-5 x + 4 y + 1
    source
    set_objective_coefficient(
+5 x + 4 y + 1
    source
    set_objective_coefficient(
     model::GenericModel{T},
     variable_1::GenericVariableRef{T},
     variable_2::GenericVariableRef{T},
@@ -2149,7 +2149,7 @@
 julia> set_objective_coefficient(model, x[1], x[2], 3)
 
 julia> objective_function(model)
-2 x[1]² + 3 x[1]*x[2]
    source
    set_objective_coefficient(
+2 x[1]² + 3 x[1]*x[2]
    source
    set_objective_coefficient(
     model::GenericModel{T},
     variables_1::AbstractVector{<:GenericVariableRef{T}},
     variables_2::AbstractVector{<:GenericVariableRef{T}},
@@ -2164,7 +2164,7 @@
 julia> set_objective_coefficient(model, [x[1], x[1]], [x[1], x[2]], [2, 3])
 
 julia> objective_function(model)
-2 x[1]² + 3 x[1]*x[2]
    source

    set_objective_function

    set_objective_function

    JuMP.set_objective_function — Function
    set_objective_function(model::GenericModel, func::MOI.AbstractFunction)
 set_objective_function(model::GenericModel, func::AbstractJuMPScalar)
 set_objective_function(model::GenericModel, func::Real)
 set_objective_function(model::GenericModel, func::Vector{<:AbstractJuMPScalar})

    Sets the objective function of the model to the given function.

    See set_objective_sense to set the objective sense.

    These are low-level functions; the recommended way to set the objective is with the @objective macro.

    Example

    julia> model = Model();
@@ -2179,7 +2179,7 @@
 julia> set_objective_function(model, 2 * x + 1)
 
 julia> objective_function(model)
-2 x + 1
    source

    set_objective_sense

    JuMP.set_objective_sense — Function
    set_objective_sense(model::GenericModel, sense::MOI.OptimizationSense)

    Sets the objective sense of the model to the given sense.

    See set_objective_function to set the objective function.

    These are low-level functions; the recommended way to set the objective is with the @objective macro.

    Example

    julia> model = Model();
+2 x + 1
    source

    set_objective_sense

    JuMP.set_objective_sense — Function
    set_objective_sense(model::GenericModel, sense::MOI.OptimizationSense)

    Sets the objective sense of the model to the given sense.

    See set_objective_function to set the objective function.

    These are low-level functions; the recommended way to set the objective is with the @objective macro.

    Example

    julia> model = Model();
 
 julia> objective_sense(model)
 FEASIBILITY_SENSE::OptimizationSense = 2
@@ -2187,7 +2187,7 @@
 julia> set_objective_sense(model, MOI.MAX_SENSE)
 
 julia> objective_sense(model)
-MAX_SENSE::OptimizationSense = 1
    source

    set_optimize_hook

    JuMP.set_optimize_hook — Function
    set_optimize_hook(model::GenericModel, f::Union{Function,Nothing})

    Set the function f as the optimize hook for model.

    f should have a signature f(model::GenericModel; kwargs...), where the kwargs are those passed to optimize!.

    Notes

    • The optimize hook should generally modify the model, or some external state in some way, and then call optimize!(model; ignore_optimize_hook = true) to optimize the problem, bypassing the hook.
    • Use set_optimize_hook(model, nothing) to unset an optimize hook.

    Example

    julia> model = Model();
+MAX_SENSE::OptimizationSense = 1
    source

    set_optimize_hook

    JuMP.set_optimize_hook — Function
    set_optimize_hook(model::GenericModel, f::Union{Function,Nothing})

    Set the function f as the optimize hook for model.

    f should have a signature f(model::GenericModel; kwargs...), where the kwargs are those passed to optimize!.

    Notes

    • The optimize hook should generally modify the model, or some external state in some way, and then call optimize!(model; ignore_optimize_hook = true) to optimize the problem, bypassing the hook.
    • Use set_optimize_hook(model, nothing) to unset an optimize hook.

    Example

    julia> model = Model();
 
 julia> function my_hook(model::Model; kwargs...)
            println(kwargs)
@@ -2204,7 +2204,7 @@
 Base.Pairs{Symbol, Bool, Tuple{Symbol}, @NamedTuple{test_arg::Bool}}(:test_arg => 1)
 Calling with `ignore_optimize_hook = true`
 ERROR: NoOptimizer()
-[...]
    source

    set_optimizer

    set_optimizer

    JuMP.set_optimizer — Function
    set_optimizer(
     model::GenericModel,
     optimizer_factory;
     add_bridges::Bool = true,
@@ -2214,7 +2214,7 @@
 
 julia> set_optimizer(model, () -> HiGHS.Optimizer())
 
-julia> set_optimizer(model, HiGHS.Optimizer; add_bridges = false)
    source

    set_parameter_value

    set_parameter_value

    JuMP.set_parameter_value — Function
    set_parameter_value(x::GenericVariableRef, value)

    Update the parameter constraint on the variable x to value.

    Errors if x is not a parameter.

    See also ParameterRef, is_parameter, parameter_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, p in Parameter(2))
 p
@@ -2225,7 +2225,7 @@
 julia> set_parameter_value(p, 2.5)
 
 julia> parameter_value(p)
-2.5
    source

    set_silent

    JuMP.set_silent — Function
    set_silent(model::GenericModel)

    Takes precedence over any other attribute controlling verbosity and requires the solver to produce no output.

    See also: unset_silent.

    Example

    julia> import Ipopt
+2.5
    source

    set_silent

    JuMP.set_silent — Function
    set_silent(model::GenericModel)

    Takes precedence over any other attribute controlling verbosity and requires the solver to produce no output.

    See also: unset_silent.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
@@ -2237,7 +2237,7 @@
 julia> unset_silent(model)
 
 julia> get_attribute(model, MOI.Silent())
-false
    source

    set_start_value

    set_start_value

    JuMP.set_start_value — Function
    set_start_value(con_ref::ConstraintRef, value)

    Set the primal start value (MOI.ConstraintPrimalStart) of the constraint con_ref to value.

    To remove a primal start value set it to nothing.

    See also start_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, start = 2.0);
 
@@ -2252,7 +2252,7 @@
 
 julia> set_start_value(c, nothing)
 
-julia> start_value(c)
    source
    set_start_value(variable::GenericVariableRef, value::Union{Real,Nothing})

    Set the start value (MOI.VariablePrimalStart) of the variable to value.

    Pass nothing to unset the start value.

    Note: VariablePrimalStarts are sometimes called "MIP-starts" or "warmstarts".

    See also: has_start_value, start_value.

    Example

    julia> model = Model();
+julia> start_value(c)
    source
    set_start_value(variable::GenericVariableRef, value::Union{Real,Nothing})

    Set the start value (MOI.VariablePrimalStart) of the variable to value.

    Pass nothing to unset the start value.

    Note: VariablePrimalStarts are sometimes called "MIP-starts" or "warmstarts".

    See also: has_start_value, start_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, start = 1.5);
 
@@ -2278,13 +2278,13 @@
 true
 
 julia> start_value(y)
-2.0
    source

    set_start_values

    set_start_values

    JuMP.set_start_values — Function
    set_start_values(
     model::GenericModel;
     variable_primal_start::Union{Nothing,Function} = value,
     constraint_primal_start::Union{Nothing,Function} = value,
     constraint_dual_start::Union{Nothing,Function} = dual,
     nonlinear_dual_start::Union{Nothing,Function} = nonlinear_dual_start_value,
-)

    Set the primal and dual starting values in model using the functions provided.

    If any keyword argument is nothing, the corresponding start value is skipped.

    If the optimizer does not support setting the starting value, the value will be skipped.

    variable_primal_start

    This function controls the primal starting solution for the variables. It is equivalent to calling set_start_value for each variable, or setting the MOI.VariablePrimalStart attribute.

    If it is a function, it must have the form variable_primal_start(x::VariableRef) that maps each variable x to the starting primal value.

    The default is value.

    constraint_primal_start

    This function controls the primal starting solution for the constraints. It is equivalent to calling set_start_value for each constraint, or setting the MOI.ConstraintPrimalStart attribute.

    If it is a function, it must have the form constraint_primal_start(ci::ConstraintRef) that maps each constraint ci to the starting primal value.

    The default is value.

    constraint_dual_start

    This function controls the dual starting solution for the constraints. It is equivalent to calling set_dual_start_value for each constraint, or setting the MOI.ConstraintDualStart attribute.

    If it is a function, it must have the form constraint_dual_start(ci::ConstraintRef) that maps each constraint ci to the starting dual value.

    The default is dual.

    nonlinear_dual_start

    This function controls the dual starting solution for the nonlinear constraints It is equivalent to calling set_nonlinear_dual_start_value.

    If it is a function, it must have the form nonlinear_dual_start(model::GenericModel) that returns a vector corresponding to the dual start of the constraints.

    The default is nonlinear_dual_start_value.

    source

    set_string_names_on_creation

    JuMP.set_string_names_on_creation — Function
    set_string_names_on_creation(model::GenericModel, value::Bool)

    Set the default argument of the set_string_name keyword in the @variable and @constraint macros to value.

    The set_string_name keyword is used to determine whether to assign String names to all variables and constraints in model.

    By default, value is true. However, for larger models calling set_string_names_on_creation(model, false) can improve performance at the cost of reducing the readability of printing and solver log messages.

    Example

    julia> import HiGHS
+)

    Set the primal and dual starting values in model using the functions provided.

    If any keyword argument is nothing, the corresponding start value is skipped.

    If the optimizer does not support setting the starting value, the value will be skipped.

    variable_primal_start

    This function controls the primal starting solution for the variables. It is equivalent to calling set_start_value for each variable, or setting the MOI.VariablePrimalStart attribute.

    If it is a function, it must have the form variable_primal_start(x::VariableRef) that maps each variable x to the starting primal value.

    The default is value.

    constraint_primal_start

    This function controls the primal starting solution for the constraints. It is equivalent to calling set_start_value for each constraint, or setting the MOI.ConstraintPrimalStart attribute.

    If it is a function, it must have the form constraint_primal_start(ci::ConstraintRef) that maps each constraint ci to the starting primal value.

    The default is value.

    constraint_dual_start

    This function controls the dual starting solution for the constraints. It is equivalent to calling set_dual_start_value for each constraint, or setting the MOI.ConstraintDualStart attribute.

    If it is a function, it must have the form constraint_dual_start(ci::ConstraintRef) that maps each constraint ci to the starting dual value.

    The default is dual.

    nonlinear_dual_start

    This function controls the dual starting solution for the nonlinear constraints It is equivalent to calling set_nonlinear_dual_start_value.

    If it is a function, it must have the form nonlinear_dual_start(model::GenericModel) that returns a vector corresponding to the dual start of the constraints.

    The default is nonlinear_dual_start_value.

    source

    set_string_names_on_creation

    JuMP.set_string_names_on_creation — Function
    set_string_names_on_creation(model::GenericModel, value::Bool)

    Set the default argument of the set_string_name keyword in the @variable and @constraint macros to value.

    The set_string_name keyword is used to determine whether to assign String names to all variables and constraints in model.

    By default, value is true. However, for larger models calling set_string_names_on_creation(model, false) can improve performance at the cost of reducing the readability of printing and solver log messages.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -2294,7 +2294,7 @@
 julia> set_string_names_on_creation(model, false)
 
 julia> set_string_names_on_creation(model)
-false
    source

    set_time_limit_sec

    set_time_limit_sec

    set_upper_bound

    set_upper_bound

    shadow_price

    JuMP.shadow_price — Function
    shadow_price(con_ref::ConstraintRef)

    Return the change in the objective from an infinitesimal relaxation of the constraint.

    The shadow price is computed from dual and can be queried only when has_duals is true and the objective sense is MIN_SENSE or MAX_SENSE (not FEASIBILITY_SENSE).

    See also reduced_cost.

    Comparison to dual

    The shadow prices differ at most in sign from the dual value depending on the objective sense. The differences are summarized in the table:

    MinMax
    f(x) <= b+1-1
    f(x) >= b-1+1

    Notes

    • The function simply translates signs from dual and does not validate the conditions needed to guarantee the sensitivity interpretation of the shadow price. The caller is responsible, for example, for checking whether the solver converged to an optimal primal-dual pair or a proof of infeasibility.
    • The computation is based on the current objective sense of the model. If this has changed since the last solve, the results will be incorrect.
    • Relaxation of equality constraints (and hence the shadow price) is defined based on which sense of the equality constraint is active.

    Example

    julia> import HiGHS
+2.0
    source

    shadow_price

    JuMP.shadow_price — Function
    shadow_price(con_ref::ConstraintRef)

    Return the change in the objective from an infinitesimal relaxation of the constraint.

    The shadow price is computed from dual and can be queried only when has_duals is true and the objective sense is MIN_SENSE or MAX_SENSE (not FEASIBILITY_SENSE).

    See also reduced_cost.

    Comparison to dual

    The shadow prices differ at most in sign from the dual value depending on the objective sense. The differences are summarized in the table:

    MinMax
    f(x) <= b+1-1
    f(x) >= b-1+1

    Notes

    • The function simply translates signs from dual and does not validate the conditions needed to guarantee the sensitivity interpretation of the shadow price. The caller is responsible, for example, for checking whether the solver converged to an optimal primal-dual pair or a proof of infeasibility.
    • The computation is based on the current objective sense of the model. If this has changed since the last solve, the results will be incorrect.
    • Relaxation of equality constraints (and hence the shadow price) is defined based on which sense of the equality constraint is active.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -2336,7 +2336,7 @@
 true
 
 julia> shadow_price(c)
-2.0
    source

    shape

    JuMP.shape — Function
    shape(c::AbstractConstraint)::AbstractShape

    Return the shape of the constraint c.

    Example

    julia> model = Model();
+2.0
    source

    shape

    JuMP.shape — Function
    shape(c::AbstractConstraint)::AbstractShape

    Return the shape of the constraint c.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -2348,20 +2348,20 @@
 julia> d = @constraint(model, x in SOS1());
 
 julia> shape(constraint_object(d))
-VectorShape()
    source

    show_backend_summary

    JuMP.show_backend_summary — Function
    show_backend_summary(io::IO, model::GenericModel)

    Print a summary of the optimizer backing model.

    Extensions

    AbstractModels should implement this method.

    Example

    julia> model = Model();
+VectorShape()
    source

    show_backend_summary

    JuMP.show_backend_summary — Function
    show_backend_summary(io::IO, model::GenericModel)

    Print a summary of the optimizer backing model.

    Extensions

    AbstractModels should implement this method.

    Example

    julia> model = Model();
 
 julia> show_backend_summary(stdout, model)
 Model mode: AUTOMATIC
 CachingOptimizer state: NO_OPTIMIZER
-Solver name: No optimizer attached.
    source

    show_constraints_summary

    JuMP.show_constraints_summary — Function
    show_constraints_summary(io::IO, model::AbstractModel)

    Write to io a summary of the number of constraints.

    Extensions

    AbstractModels should implement this method.

    Example

    julia> model = Model();
+Solver name: No optimizer attached.
    source

    show_constraints_summary

    JuMP.show_constraints_summary — Function
    show_constraints_summary(io::IO, model::AbstractModel)

    Write to io a summary of the number of constraints.

    Extensions

    AbstractModels should implement this method.

    Example

    julia> model = Model();
 
 julia> @variable(model, x >= 0);
 
 julia> show_constraints_summary(stdout, model)
-`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 1 constraint
    source

    show_objective_function_summary

    JuMP.show_objective_function_summary — Function
    show_objective_function_summary(io::IO, model::AbstractModel)

    Write to io a summary of the objective function type.

    Extensions

    AbstractModels should implement this method.

    Example

    julia> model = Model();
+`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 1 constraint
    source

    show_objective_function_summary

    JuMP.show_objective_function_summary — Function
    show_objective_function_summary(io::IO, model::AbstractModel)

    Write to io a summary of the objective function type.

    Extensions

    AbstractModels should implement this method.

    Example

    julia> model = Model();
 
 julia> show_objective_function_summary(stdout, model)
-Objective function type: AffExpr
    source

    simplex_iterations

    JuMP.simplex_iterations — Function
    simplex_iterations(model::GenericModel)

    If available, returns the cumulative number of simplex iterations during the most-recent optimization (the MOI.SimplexIterations attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
+Objective function type: AffExpr
    source

    simplex_iterations

    JuMP.simplex_iterations — Function
    simplex_iterations(model::GenericModel)

    If available, returns the cumulative number of simplex iterations during the most-recent optimization (the MOI.SimplexIterations attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -2370,7 +2370,7 @@
 julia> optimize!(model)
 
 julia> simplex_iterations(model)
-0
    source

    solution_summary

    JuMP.solution_summary — Function
    solution_summary(model::GenericModel; result::Int = 1, verbose::Bool = false)

    Return a struct that can be used print a summary of the solution in result result.

    If verbose=true, write out the primal solution for every variable and the dual solution for every constraint, excluding those with empty names.

    Example

    When called at the REPL, the summary is automatically printed:

    julia> model = Model();
+0
    source

    solution_summary

    JuMP.solution_summary — Function
    solution_summary(model::GenericModel; result::Int = 1, verbose::Bool = false)

    Return a struct that can be used print a summary of the solution in result result.

    If verbose=true, write out the primal solution for every variable and the dual solution for every constraint, excluding those with empty names.

    Example

    When called at the REPL, the summary is automatically printed:

    julia> model = Model();
 
 julia> solution_summary(model)
 * Solver : No optimizer attached.
@@ -2406,7 +2406,7 @@
   Primal status      : NO_SOLUTION
   Dual status        : NO_SOLUTION
 
-* Work counters
    source

    solve_time

    JuMP.solve_time — Function
    solve_time(model::GenericModel)

    If available, returns the solve time in wall-clock seconds reported by the solver (the MOI.SolveTimeSec attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
+* Work counters
    source

    solve_time

    JuMP.solve_time — Function
    solve_time(model::GenericModel)

    If available, returns the solve time in wall-clock seconds reported by the solver (the MOI.SolveTimeSec attribute).

    Throws a MOI.GetAttributeNotAllowed error if the attribute is not implemented by the solver.

    Example

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer);
 
@@ -2415,7 +2415,7 @@
 julia> optimize!(model)
 
 julia> solve_time(model)
-1.0488089174032211e-5
    source

    solver_name

    JuMP.solver_name — Function
    solver_name(model::GenericModel)

    If available, returns the MOI.SolverName property of the underlying optimizer.

    Returns "No optimizer attached." in AUTOMATIC or MANUAL modes when no optimizer is attached.

    Returns "SolverName() attribute not implemented by the optimizer." if the attribute is not implemented.

    Example

    julia> import Ipopt
+1.0488089174032211e-5
    source

    solver_name

    JuMP.solver_name — Function
    solver_name(model::GenericModel)

    If available, returns the MOI.SolverName property of the underlying optimizer.

    Returns "No optimizer attached." in AUTOMATIC or MANUAL modes when no optimizer is attached.

    Returns "SolverName() attribute not implemented by the optimizer." if the attribute is not implemented.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
@@ -2430,7 +2430,7 @@
 julia> model = Model(MOI.FileFormats.MPS.Model);
 
 julia> solver_name(model)
-"SolverName() attribute not implemented by the optimizer."
    source

    start_value

    JuMP.start_value — Function
    start_value(con_ref::ConstraintRef)

    Return the primal start value (MOI.ConstraintPrimalStart) of the constraint con_ref.

    If no primal start value has been set, start_value will return nothing.

    See also set_start_value.

    Example

    julia> model = Model();
+"SolverName() attribute not implemented by the optimizer."
    source

    start_value

    JuMP.start_value — Function
    start_value(con_ref::ConstraintRef)

    Return the primal start value (MOI.ConstraintPrimalStart) of the constraint con_ref.

    If no primal start value has been set, start_value will return nothing.

    See also set_start_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, start = 2.0);
 
@@ -2445,7 +2445,7 @@
 
 julia> set_start_value(c, nothing)
 
-julia> start_value(c)
    source
    start_value(v::GenericVariableRef)

    Return the start value (MOI.VariablePrimalStart) of the variable v.

    Note: VariablePrimalStarts are sometimes called "MIP-starts" or "warmstarts".

    See also: has_start_value, set_start_value.

    Example

    julia> model = Model();
+julia> start_value(c)
    source
    start_value(v::GenericVariableRef)

    Return the start value (MOI.VariablePrimalStart) of the variable v.

    Note: VariablePrimalStarts are sometimes called "MIP-starts" or "warmstarts".

    See also: has_start_value, set_start_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, start = 1.5);
 
@@ -2466,12 +2466,12 @@
 true
 
 julia> start_value(y)
-2.0
    source

    termination_status

    termination_status

    time_limit_sec

    time_limit_sec

    JuMP.time_limit_sec — Function
    time_limit_sec(model::GenericModel)

    Return the time limit (in seconds) of the model.

    Returns nothing if unset.

    See also: set_time_limit_sec, unset_time_limit_sec.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
@@ -2484,7 +2484,7 @@
 
 julia> unset_time_limit_sec(model)
 
-julia> time_limit_sec(model)
    source

    triangle_vec

    JuMP.triangle_vec — Function
    triangle_vec(matrix::Matrix)

    Return the upper triangle of a matrix concatenated into a vector in the order required by JuMP and MathOptInterface for Triangle sets.

    Example

    julia> model = Model();
+julia> time_limit_sec(model)
    source

    triangle_vec

    JuMP.triangle_vec — Function
    triangle_vec(matrix::Matrix)

    Return the upper triangle of a matrix concatenated into a vector in the order required by JuMP and MathOptInterface for Triangle sets.

    Example

    julia> model = Model();
 
 julia> @variable(model, X[1:3, 1:3], Symmetric);
 
@@ -2492,7 +2492,7 @@
 t
 
 julia> @constraint(model, [t; triangle_vec(X)] in MOI.RootDetConeTriangle(3))
-[t, X[1,1], X[1,2], X[2,2], X[1,3], X[2,3], X[3,3]] ∈ MathOptInterface.RootDetConeTriangle(3)
    source

    unfix

    JuMP.unfix — Function
    unfix(v::GenericVariableRef)

    Delete the fixing constraint of a variable.

    Error if one does not exist.

    See also FixRef, is_fixed, fix_value, fix.

    Example

    julia> model = Model();
+[t, X[1,1], X[1,2], X[2,2], X[1,3], X[2,3], X[3,3]] ∈ MathOptInterface.RootDetConeTriangle(3)
    source

    unfix

    JuMP.unfix — Function
    unfix(v::GenericVariableRef)

    Delete the fixing constraint of a variable.

    Error if one does not exist.

    See also FixRef, is_fixed, fix_value, fix.

    Example

    julia> model = Model();
 
 julia> @variable(model, x == 1);
 
@@ -2502,7 +2502,7 @@
 julia> unfix(x)
 
 julia> is_fixed(x)
-false
    source

    unregister

    JuMP.unregister — Function
    unregister(model::GenericModel, key::Symbol)

    Unregister the name key from model so that a new variable, constraint, or expression can be created with the same key.

    Note that this will not delete the object model[key]; it will just remove the reference at model[key]. To delete the object, use delete as well.

    See also: delete, object_dictionary.

    Example

    julia> model = Model();
+false
    source

    unregister

    JuMP.unregister — Function
    unregister(model::GenericModel, key::Symbol)

    Unregister the name key from model so that a new variable, constraint, or expression can be created with the same key.

    Note that this will not delete the object model[key]; it will just remove the reference at model[key]. To delete the object, use delete as well.

    See also: delete, object_dictionary.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -2529,7 +2529,7 @@
 x
 
 julia> num_variables(model)
-2
    source

    unsafe_backend

    JuMP.unsafe_backend — Function
    unsafe_backend(model::GenericModel)

    Return the innermost optimizer associated with the JuMP model model.

    This function should only be used by advanced users looking to access low-level solver-specific functionality. It has a high-risk of incorrect usage. We strongly suggest you use the alternative suggested below.

    See also: backend.

    To obtain the index of a variable or constraint in the unsafe backend, use optimizer_index.

    Unsafe behavior

    This function is unsafe for two main reasons.

    First, the formulation and order of variables and constraints in the unsafe backend may be different to the variables and constraints in model. This can happen because of bridges, or because the solver requires the variables or constraints in a specific order. In addition, the variable or constraint index returned by index at the JuMP level may be different to the index of the corresponding variable or constraint in the unsafe_backend. There is no solution to this. Use the alternative suggested below instead.

    Second, the unsafe_backend may be empty, or lack some modifications made to the JuMP model. Thus, before calling unsafe_backend you should first call MOI.Utilities.attach_optimizer to ensure that the backend is synchronized with the JuMP model.

    julia> import HiGHS
+2
    source

    unsafe_backend

    JuMP.unsafe_backend — Function
    unsafe_backend(model::GenericModel)

    Return the innermost optimizer associated with the JuMP model model.

    This function should only be used by advanced users looking to access low-level solver-specific functionality. It has a high-risk of incorrect usage. We strongly suggest you use the alternative suggested below.

    See also: backend.

    To obtain the index of a variable or constraint in the unsafe backend, use optimizer_index.

    Unsafe behavior

    This function is unsafe for two main reasons.

    First, the formulation and order of variables and constraints in the unsafe backend may be different to the variables and constraints in model. This can happen because of bridges, or because the solver requires the variables or constraints in a specific order. In addition, the variable or constraint index returned by index at the JuMP level may be different to the index of the corresponding variable or constraint in the unsafe_backend. There is no solution to this. Use the alternative suggested below instead.

    Second, the unsafe_backend may be empty, or lack some modifications made to the JuMP model. Thus, before calling unsafe_backend you should first call MOI.Utilities.attach_optimizer to ensure that the backend is synchronized with the JuMP model.

    julia> import HiGHS
 
 julia> model = Model(HiGHS.Optimizer)
 A JuMP Model
@@ -2570,7 +2570,7 @@
 A HiGHS model with 1 columns and 0 rows.
 
 julia> index(x)
-MOI.VariableIndex(1)
    source

    unset_binary

    unset_binary

    JuMP.unset_binary — Function
    unset_binary(variable_ref::GenericVariableRef)

    Remove the binary constraint on the variable variable_ref.

    See also BinaryRef, is_binary, set_binary.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, Bin);
 
@@ -2580,7 +2580,7 @@
 julia> unset_binary(x)
 
 julia> is_binary(x)
-false
    source

    unset_integer

    unset_integer

    JuMP.unset_integer — Function
    unset_integer(variable_ref::GenericVariableRef)

    Remove the integrality constraint on the variable variable_ref.

    Errors if one does not exist.

    See also IntegerRef, is_integer, set_integer.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, Int);
 
@@ -2590,7 +2590,7 @@
 julia> unset_integer(x)
 
 julia> is_integer(x)
-false
    source

    unset_silent

    JuMP.unset_silent — Function
    unset_silent(model::GenericModel)

    Neutralize the effect of the set_silent function and let the solver attributes control the verbosity.

    See also: set_silent.

    Example

    julia> import Ipopt
+false
    source

    unset_silent

    JuMP.unset_silent — Function
    unset_silent(model::GenericModel)

    Neutralize the effect of the set_silent function and let the solver attributes control the verbosity.

    See also: set_silent.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
@@ -2602,7 +2602,7 @@
 julia> unset_silent(model)
 
 julia> get_attribute(model, MOI.Silent())
-false
    source

    unset_time_limit_sec

    unset_time_limit_sec

    JuMP.unset_time_limit_sec — Function
    unset_time_limit_sec(model::GenericModel)

    Unset the time limit of the solver.

    See also: set_time_limit_sec, time_limit_sec.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
@@ -2615,19 +2615,19 @@
 
 julia> unset_time_limit_sec(model)
 
-julia> time_limit_sec(model)
    source

    upper_bound

    upper_bound

    value

    JuMP.value — Function
    value(con_ref::ConstraintRef; result::Int = 1)

    Return the primal value of constraint con_ref associated with result index result of the most-recent solution returned by the solver.

    That is, if con_ref is the reference of a constraint func-in-set, it returns the value of func evaluated at the value of the variables (given by value(::GenericVariableRef)).

    Use has_values to check if a result exists before asking for values.

    See also: result_count.

    Note

    For scalar constraints, the constant is moved to the set so it is not taken into account in the primal value of the constraint. For instance, the constraint @constraint(model, 2x + 3y + 1 == 5) is transformed into 2x + 3y-in-MOI.EqualTo(4) so the value returned by this function is the evaluation of 2x + 3y.

    source
    value(var_value::Function, con_ref::ConstraintRef)

    Evaluate the primal value of the constraint con_ref using var_value(v) as the value for each variable v.

    source
    value(v::GenericVariableRef; result = 1)

    Return the value of variable v associated with result index result of the most-recent returned by the solver.

    Use has_values to check if a result exists before asking for values.

    See also: result_count.

    source
    value(var_value::Function, v::GenericVariableRef)

    Evaluate the value of the variable v as var_value(v).

    source
    value(var_value::Function, ex::GenericAffExpr)

    Evaluate ex using var_value(v) as the value for each variable v.

    source
    value(v::GenericAffExpr; result::Int = 1)

    Return the value of the GenericAffExpr v associated with result index result of the most-recent solution returned by the solver.

    See also: result_count.

    source
    value(var_value::Function, ex::GenericQuadExpr)

    Evaluate ex using var_value(v) as the value for each variable v.

    source
    value(v::GenericQuadExpr; result::Int = 1)

    Return the value of the GenericQuadExpr v associated with result index result of the most-recent solution returned by the solver.

    Replaces getvalue for most use cases.

    See also: result_count.

    source
    value(p::NonlinearParameter)

    Return the current value stored in the nonlinear parameter p.

    Example

    julia> model = Model();
+1.0
    source

    value

    JuMP.value — Function
    value(con_ref::ConstraintRef; result::Int = 1)

    Return the primal value of constraint con_ref associated with result index result of the most-recent solution returned by the solver.

    That is, if con_ref is the reference of a constraint func-in-set, it returns the value of func evaluated at the value of the variables (given by value(::GenericVariableRef)).

    Use has_values to check if a result exists before asking for values.

    See also: result_count.

    Note

    For scalar constraints, the constant is moved to the set so it is not taken into account in the primal value of the constraint. For instance, the constraint @constraint(model, 2x + 3y + 1 == 5) is transformed into 2x + 3y-in-MOI.EqualTo(4) so the value returned by this function is the evaluation of 2x + 3y.

    source
    value(var_value::Function, con_ref::ConstraintRef)

    Evaluate the primal value of the constraint con_ref using var_value(v) as the value for each variable v.

    source
    value(v::GenericVariableRef; result = 1)

    Return the value of variable v associated with result index result of the most-recent returned by the solver.

    Use has_values to check if a result exists before asking for values.

    See also: result_count.

    source
    value(var_value::Function, v::GenericVariableRef)

    Evaluate the value of the variable v as var_value(v).

    source
    value(var_value::Function, ex::GenericAffExpr)

    Evaluate ex using var_value(v) as the value for each variable v.

    source
    value(v::GenericAffExpr; result::Int = 1)

    Return the value of the GenericAffExpr v associated with result index result of the most-recent solution returned by the solver.

    See also: result_count.

    source
    value(var_value::Function, ex::GenericQuadExpr)

    Evaluate ex using var_value(v) as the value for each variable v.

    source
    value(v::GenericQuadExpr; result::Int = 1)

    Return the value of the GenericQuadExpr v associated with result index result of the most-recent solution returned by the solver.

    Replaces getvalue for most use cases.

    See also: result_count.

    source
    value(p::NonlinearParameter)

    Return the current value stored in the nonlinear parameter p.

    Example

    julia> model = Model();
 
 julia> @NLparameter(model, p == 10)
 p == 10.0
 
 julia> value(p)
-10.0
    source
    value(ex::NonlinearExpression; result::Int = 1)

    Return the value of the NonlinearExpression ex associated with result index result of the most-recent solution returned by the solver.

    See also: result_count.

    source
    value(var_value::Function, ex::NonlinearExpression)

    Evaluate ex using var_value(v) as the value for each variable v.

    source
    value(c::NonlinearConstraintRef; result::Int = 1)

    Return the value of the NonlinearConstraintRef c associated with result index result of the most-recent solution returned by the solver.

    See also: result_count.

    source
    value(var_value::Function, c::NonlinearConstraintRef)

    Evaluate c using var_value(v) as the value for each variable v.

    source

    value_type

    JuMP.value_type — Function
    value_type(::Type{<:Union{AbstractModel,AbstractVariableRef}})

    Return the return type of value for variables of that model. It defaults to Float64 if it is not implemented.

    Example

    julia> value_type(GenericModel{BigFloat})
-BigFloat
    source

    variable_by_name

    JuMP.variable_by_name — Function
    variable_by_name(
+10.0
    source
    value(ex::NonlinearExpression; result::Int = 1)

    Return the value of the NonlinearExpression ex associated with result index result of the most-recent solution returned by the solver.

    See also: result_count.

    source
    value(var_value::Function, ex::NonlinearExpression)

    Evaluate ex using var_value(v) as the value for each variable v.

    source
    value(c::NonlinearConstraintRef; result::Int = 1)

    Return the value of the NonlinearConstraintRef c associated with result index result of the most-recent solution returned by the solver.

    See also: result_count.

    source
    value(var_value::Function, c::NonlinearConstraintRef)

    Evaluate c using var_value(v) as the value for each variable v.

    source

    value_type

    JuMP.value_type — Function
    value_type(::Type{<:Union{AbstractModel,AbstractVariableRef}})

    Return the return type of value for variables of that model. It defaults to Float64 if it is not implemented.

    Example

    julia> value_type(GenericModel{BigFloat})
+BigFloat
    source

    variable_by_name

    JuMP.variable_by_name — Function
    variable_by_name(
     model::AbstractModel,
     name::String,
 )::Union{AbstractVariableRef,Nothing}

    Returns the reference of the variable with name attribute name or Nothing if no variable has this name attribute. Throws an error if several variables have name as their name attribute.

    Example

    julia> model = Model();
@@ -2670,12 +2670,12 @@
  u[2]
 
 julia> variable_by_name(model, "u[2]")
-u[2]
    source

    variable_ref_type

    JuMP.variable_ref_type — Function
    variable_ref_type(::Union{F,Type{F}}) where {F}

    A helper function used internally by JuMP and some JuMP extensions. Returns the variable type associated with the model or expression type F.

    source

    vectorize

    JuMP.vectorize — Function
    vectorize(matrix::AbstractMatrix, ::Shape)

    Convert the matrix into a vector according to Shape.

    source

    write_to_file

    variable_ref_type

    JuMP.variable_ref_type — Function
    variable_ref_type(::Union{F,Type{F}}) where {F}

    A helper function used internally by JuMP and some JuMP extensions. Returns the variable type associated with the model or expression type F.

    source

    vectorize

    JuMP.vectorize — Function
    vectorize(matrix::AbstractMatrix, ::Shape)

    Convert the matrix into a vector according to Shape.

    source

    write_to_file

    JuMP.write_to_file — Function
    write_to_file(
     model::GenericModel,
     filename::String;
     format::MOI.FileFormats.FileFormat = MOI.FileFormats.FORMAT_AUTOMATIC,
     kwargs...,
-)

    Write the JuMP model model to filename in the format format.

    If the filename ends in .gz, it will be compressed using GZip. If the filename ends in .bz2, it will be compressed using BZip2.

    Other kwargs are passed to the Model constructor of the chosen format.

    source

    AbstractConstraint

    JuMP.AbstractConstraint — Type
    abstract type AbstractConstraint

    An abstract base type for all constraint types. AbstractConstraints store the function and set directly, unlike ConstraintRefs that are merely references to constraints stored in a model. AbstractConstraints do not need to be attached to a model.

    source

    AbstractJuMPScalar

    JuMP.AbstractJuMPScalar — Type
    AbstractJuMPScalar <: MutableArithmetics.AbstractMutable

    Abstract base type for all scalar types

    The subtyping of AbstractMutable will allow calls of some Base functions to be redirected to a method in MA that handles type promotion more carefully (for example the promotion in sparse matrix products in SparseArrays usually does not work for JuMP types) and exploits the mutability of AffExpr and QuadExpr.

    source

    AbstractModel

    JuMP.AbstractModel — Type
    AbstractModel

    An abstract type that should be subtyped for users creating JuMP extensions.

    source

    AbstractScalarSet

    JuMP.AbstractScalarSet — Type
    AbstractScalarSet

    An abstract type for defining new scalar sets in JuMP.

    Implement moi_set(::AbstractScalarSet) to convert the type into an MOI set.

    See also: moi_set.

    source

    AbstractShape

    AbstractVariable

    AbstractVariableRef

    JuMP.AbstractVariableRef — Type
    AbstractVariableRef

    Variable returned by add_variable. Affine (resp. quadratic) operations with variables of type V<:AbstractVariableRef and coefficients of type T create a GenericAffExpr{T,V} (resp. GenericQuadExpr{T,V}).

    source

    AbstractVectorSet

    JuMP.AbstractVectorSet — Type
    AbstractVectorSet

    An abstract type for defining new sets in JuMP.

    Implement moi_set(::AbstractVectorSet, dim::Int) to convert the type into an MOI set.

    See also: moi_set.

    source

    AffExpr

    ArrayShape

    JuMP.ArrayShape — Type
    ArrayShape{N}(dims::NTuple{N,Int}) where {N}

    An AbstractShape that represents array-valued constraints.

    Example

    julia> model = Model();
+)

    Write the JuMP model model to filename in the format format.

    If the filename ends in .gz, it will be compressed using GZip. If the filename ends in .bz2, it will be compressed using BZip2.

    Other kwargs are passed to the Model constructor of the chosen format.

    source

    AbstractConstraint

    JuMP.AbstractConstraint — Type
    abstract type AbstractConstraint

    An abstract base type for all constraint types. AbstractConstraints store the function and set directly, unlike ConstraintRefs that are merely references to constraints stored in a model. AbstractConstraints do not need to be attached to a model.

    source

    AbstractJuMPScalar

    JuMP.AbstractJuMPScalar — Type
    AbstractJuMPScalar <: MutableArithmetics.AbstractMutable

    Abstract base type for all scalar types

    The subtyping of AbstractMutable will allow calls of some Base functions to be redirected to a method in MA that handles type promotion more carefully (for example the promotion in sparse matrix products in SparseArrays usually does not work for JuMP types) and exploits the mutability of AffExpr and QuadExpr.

    source

    AbstractModel

    JuMP.AbstractModel — Type
    AbstractModel

    An abstract type that should be subtyped for users creating JuMP extensions.

    source

    AbstractScalarSet

    JuMP.AbstractScalarSet — Type
    AbstractScalarSet

    An abstract type for defining new scalar sets in JuMP.

    Implement moi_set(::AbstractScalarSet) to convert the type into an MOI set.

    See also: moi_set.

    source

    AbstractShape

    AbstractVariable

    AbstractVariableRef

    JuMP.AbstractVariableRef — Type
    AbstractVariableRef

    Variable returned by add_variable. Affine (resp. quadratic) operations with variables of type V<:AbstractVariableRef and coefficients of type T create a GenericAffExpr{T,V} (resp. GenericQuadExpr{T,V}).

    source

    AbstractVectorSet

    JuMP.AbstractVectorSet — Type
    AbstractVectorSet

    An abstract type for defining new sets in JuMP.

    Implement moi_set(::AbstractVectorSet, dim::Int) to convert the type into an MOI set.

    See also: moi_set.

    source

    AffExpr

    ArrayShape

    JuMP.ArrayShape — Type
    ArrayShape{N}(dims::NTuple{N,Int}) where {N}

    An AbstractShape that represents array-valued constraints.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2, 1:3]);
 
@@ -2684,12 +2684,12 @@
  x[2,1]  x[2,2]  x[2,3]] ∈ Nonnegatives()
 
 julia> shape(constraint_object(c))
-ArrayShape{2}((2, 3))
    source

    BinaryRef

    JuMP.BinaryRef — Function
    BinaryRef(v::GenericVariableRef)

    Return a constraint reference to the constraint constraining v to be binary. Errors if one does not exist.

    See also is_binary, set_binary, unset_binary.

    Example

    julia> model = Model();
+ArrayShape{2}((2, 3))
    source

    BinaryRef

    JuMP.BinaryRef — Function
    BinaryRef(v::GenericVariableRef)

    Return a constraint reference to the constraint constraining v to be binary. Errors if one does not exist.

    See also is_binary, set_binary, unset_binary.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, Bin);
 
 julia> BinaryRef(x)
-x binary
    source

    BridgeableConstraint

    BridgeableConstraint

    JuMP.BridgeableConstraint — Type
    BridgeableConstraint(
     constraint::C,
     bridge_type::B;
     coefficient_type::Type{T} = Float64,
@@ -2704,7 +2704,7 @@
 )
     constraint = ScalarConstraint(func, set)
     return BridgeableConstraint(constraint, CustomBridge)
-end

    Note

    JuMP extensions should extend JuMP.build_constraint only if they also defined CustomSet, for three reasons:

    1. It is problematic if multiple extensions overload the same JuMP method.
    2. A missing method will not inform the users that they forgot to load the extension module defining the build_constraint method.
    3. Defining a method where neither the function nor any of the argument types are defined in the package is called type piracy and is discouraged in the Julia style guide.
    source

    ComplexPlane

    JuMP.ComplexPlane — Type
    ComplexPlane

    Complex plane object that can be used to create a complex variable in the @variable macro.

    Example

    Consider the following example:

    julia> model = Model();
+end

    Note

    JuMP extensions should extend JuMP.build_constraint only if they also defined CustomSet, for three reasons:

    1. It is problematic if multiple extensions overload the same JuMP method.
    2. A missing method will not inform the users that they forgot to load the extension module defining the build_constraint method.
    3. Defining a method where neither the function nor any of the argument types are defined in the package is called type piracy and is discouraged in the Julia style guide.
    source

    ComplexPlane

    JuMP.ComplexPlane — Type
    ComplexPlane

    Complex plane object that can be used to create a complex variable in the @variable macro.

    Example

    Consider the following example:

    julia> model = Model();
 
 julia> @variable(model, x in ComplexPlane())
 real(x) + imag(x) im
@@ -2712,7 +2712,7 @@
 julia> all_variables(model)
 2-element Vector{VariableRef}:
  real(x)
- imag(x)

    We see in the output of the last command that two real variables were created. The Julia variable x binds to an affine expression in terms of these two variables that parametrize the complex plane.

    source

    ComplexVariable

    ConstraintNotOwned

    JuMP.ConstraintNotOwned — Type
    struct ConstraintNotOwned{C<:ConstraintRef} <: Exception
+ imag(x)

    We see in the output of the last command that two real variables were created. The Julia variable x binds to an affine expression in terms of these two variables that parametrize the complex plane.

    source

    ComplexVariable

    ConstraintNotOwned

    JuMP.ConstraintNotOwned — Type
    struct ConstraintNotOwned{C<:ConstraintRef} <: Exception
     constraint_ref::C
 end

    An error thrown when the constraint constraint_ref was used in a model different to owner_model(constraint_ref).

    Example

    julia> model = Model();
 
@@ -2726,12 +2726,12 @@
 julia> MOI.get(model_new, MOI.ConstraintName(), c)
 ERROR: ConstraintNotOwned{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.GreaterThan{Float64}}, ScalarShape}}(c : x ≥ 0)
 Stacktrace:
-[...]
    source

    ConstraintRef

    FixRef

    JuMP.FixRef — Function
    FixRef(v::GenericVariableRef)

    Return a constraint reference to the constraint fixing the value of v.

    Errors if one does not exist.

    See also is_fixed, fix_value, fix, unfix.

    Example

    julia> model = Model();
+[...]
    source

    ConstraintRef

    FixRef

    JuMP.FixRef — Function
    FixRef(v::GenericVariableRef)

    Return a constraint reference to the constraint fixing the value of v.

    Errors if one does not exist.

    See also is_fixed, fix_value, fix, unfix.

    Example

    julia> model = Model();
 
 julia> @variable(model, x == 1);
 
 julia> FixRef(x)
-x = 1
    source

    GenericAffExpr

    GenericAffExpr

    JuMP.GenericAffExpr — Type
    mutable struct GenericAffExpr{CoefType,VarType} <: AbstractJuMPScalar
     constant::CoefType
     terms::OrderedDict{VarType,CoefType}
 end

    An expression type representing an affine expression of the form: $\sum a_i x_i + c$.

    Fields

    • .constant: the constant c in the expression.
    • .terms: an OrderedDict, with keys of VarType and values of CoefType describing the sparse vector a.

    Example

    julia> model = Model();
@@ -2747,13 +2747,13 @@
 julia> expr.terms
 OrderedCollections.OrderedDict{VariableRef, Float64} with 2 entries:
   x[2] => 1.0
-  x[1] => 3.0
    source

    GenericModel

    GenericModel

    JuMP.GenericModel — Type
    GenericModel{T}(
     [optimizer_factory;]
     add_bridges::Bool = true,
 ) where {T<:Real}

    Create a new instance of a JuMP model.

    If optimizer_factory is provided, the model is initialized with the optimizer returned by MOI.instantiate(optimizer_factory).

    If optimizer_factory is not provided, use set_optimizer to set the optimizer before calling optimize!.

    If add_bridges, JuMP adds a MOI.Bridges.LazyBridgeOptimizer to automatically reformulate the problem into a form supported by the optimizer.

    Value type T

    Passing a type other than Float64 as the value type T is an advanced operation. The value type must match that expected by the chosen optimizer. Consult the optimizers documentation for details.

    If not documented, assume that the optimizer supports only Float64.

    Choosing an unsupported value type will throw an MOI.UnsupportedConstraint or an MOI.UnsupportedAttribute error, the timing of which (during the model construction or during a call to optimize!) depends on how the solver is interfaced to JuMP.

    Example

    julia> model = GenericModel{BigFloat}();
 
 julia> typeof(model)
-GenericModel{BigFloat}
    source

    GenericNonlinearExpr

    GenericNonlinearExpr

    JuMP.GenericNonlinearExpr — Type
    GenericNonlinearExpr{V}(head::Symbol, args::Vector{Any})
 GenericNonlinearExpr{V}(head::Symbol, args::Any...)

    The scalar-valued nonlinear function head(args...), represented as a symbolic expression tree, with the call operator head and ordered arguments in args.

    V is the type of AbstractVariableRef present in the expression, and is used to help dispatch JuMP extensions.

    head

    The head::Symbol must be an operator supported by the model.

    The default list of supported univariate operators is given by:

    and the default list of supported multivariate operators is given by:

    Additional operators can be add using @operator.

    See the full list of operators supported by a MOI.ModelLike by querying the MOI.ListOfSupportedNonlinearOperators attribute.

    args

    The vector args contains the arguments to the nonlinear function. If the operator is univariate, it must contain one element. Otherwise, it may contain multiple elements.

    Given a subtype of AbstractVariableRef, V, for GenericNonlinearExpr{V}, each element must be one of the following:

    where T<:Real and T == value_type(V).

    Unsupported operators

    If the optimizer does not support head, an MOI.UnsupportedNonlinearOperator error will be thrown.

    There is no guarantee about when this error will be thrown; it may be thrown when the function is first added to the model, or it may be thrown when optimize! is called.

    Example

    To represent the function $f(x) = sin(x)^2$, do:

    julia> model = Model();
 
 julia> @variable(model, x)
@@ -2767,7 +2767,7 @@
            GenericNonlinearExpr{VariableRef}(:sin, x),
            2.0,
        )
-sin(x) ^ 2.0
    source

    GenericQuadExpr

    GenericQuadExpr

    JuMP.GenericQuadExpr — Type
    mutable struct GenericQuadExpr{CoefType,VarType} <: AbstractJuMPScalar
     aff::GenericAffExpr{CoefType,VarType}
     terms::OrderedDict{UnorderedPair{VarType}, CoefType}
 end

    An expression type representing an quadratic expression of the form: $\sum q_{i,j} x_i x_j + \sum a_i x_i + c$.

    Fields

    • .aff: an GenericAffExpr representing the affine portion of the expression.
    • .terms: an OrderedDict, with keys of UnorderedPair{VarType} and values of CoefType, describing the sparse list of terms q.

    Example

    julia> model = Model();
@@ -2783,16 +2783,16 @@
 julia> expr.terms
 OrderedCollections.OrderedDict{UnorderedPair{VariableRef}, Float64} with 2 entries:
   UnorderedPair{VariableRef}(x[1], x[1]) => 2.0
-  UnorderedPair{VariableRef}(x[1], x[2]) => 1.0
    source

    GenericReferenceMap

    JuMP.GenericReferenceMap — Type
    GenericReferenceMap{T}

    Mapping between variable and constraint reference of a model and its copy. The reference of the copied model can be obtained by indexing the map with the reference of the corresponding reference of the original model.

    source

    GenericVariableRef

    JuMP.GenericVariableRef — Type
    GenericVariableRef{T} <: AbstractVariableRef

    Holds a reference to the model and the corresponding MOI.VariableIndex.

    source

    GreaterThanZero

    JuMP.GreaterThanZero — Type
    GreaterThanZero()

    A struct used to intercept when >= or ≥ is used in a macro via operator_to_set.

    This struct is not the same as Nonnegatives so that we can disambiguate x >= y and x - y in Nonnegatives().

    This struct is not intended for general usage, but it may be useful to some JuMP extensions.

    Example

    julia> operator_to_set(error, Val(:>=))
-GreaterThanZero()
    source

    HermitianMatrixAdjointShape

    HermitianMatrixShape

    GenericReferenceMap

    JuMP.GenericReferenceMap — Type
    GenericReferenceMap{T}

    Mapping between variable and constraint reference of a model and its copy. The reference of the copied model can be obtained by indexing the map with the reference of the corresponding reference of the original model.

    source

    GenericVariableRef

    JuMP.GenericVariableRef — Type
    GenericVariableRef{T} <: AbstractVariableRef

    Holds a reference to the model and the corresponding MOI.VariableIndex.

    source

    GreaterThanZero

    JuMP.GreaterThanZero — Type
    GreaterThanZero()

    A struct used to intercept when >= or ≥ is used in a macro via operator_to_set.

    This struct is not the same as Nonnegatives so that we can disambiguate x >= y and x - y in Nonnegatives().

    This struct is not intended for general usage, but it may be useful to some JuMP extensions.

    Example

    julia> operator_to_set(error, Val(:>=))
+GreaterThanZero()
    source

    HermitianMatrixAdjointShape

    HermitianMatrixShape

    JuMP.HermitianMatrixShape — Type
    HermitianMatrixShape(
     side_dimension::Int;
     needs_adjoint_dual::Bool = false,
-)

    The shape object for a Hermitian square matrix of side_dimension rows and columns.

    The vectorized form corresponds to MOI.HermitianPositiveSemidefiniteConeTriangle.

    needs_adjoint_dual

    By default, the dual_shape of HermitianMatrixShape is also HermitianMatrixShape. This is true for cases such as a LinearAlgebra.Hermitian matrix in HermitianPSDCone.

    However, JuMP also supports LinearAlgebra.Hermitian matrix in Zeros, which is interpreted as an element-wise equality constraint. By exploiting symmetry, we pass only the upper triangle of the equality constraints. This works for the primal, but it leads to a factor of 2 difference in the off-diagonal dual elements. (The dual value of the (i, j) element in the triangle formulation should be divided by 2 when spread across the (i, j) and (j, i) elements in the square matrix formulation.) If the constraint has this dual inconsistency, set needs_adjoint_dual = true.

    source

    HermitianMatrixSpace

    JuMP.HermitianMatrixSpace — Type
    HermitianMatrixSpace()

    Use in the @variable macro to constrain a matrix of variables to be hermitian.

    Example

    julia> model = Model();
+)

    The shape object for a Hermitian square matrix of side_dimension rows and columns.

    The vectorized form corresponds to MOI.HermitianPositiveSemidefiniteConeTriangle.

    needs_adjoint_dual

    By default, the dual_shape of HermitianMatrixShape is also HermitianMatrixShape. This is true for cases such as a LinearAlgebra.Hermitian matrix in HermitianPSDCone.

    However, JuMP also supports LinearAlgebra.Hermitian matrix in Zeros, which is interpreted as an element-wise equality constraint. By exploiting symmetry, we pass only the upper triangle of the equality constraints. This works for the primal, but it leads to a factor of 2 difference in the off-diagonal dual elements. (The dual value of the (i, j) element in the triangle formulation should be divided by 2 when spread across the (i, j) and (j, i) elements in the square matrix formulation.) If the constraint has this dual inconsistency, set needs_adjoint_dual = true.

    source

    HermitianMatrixSpace

    JuMP.HermitianMatrixSpace — Type
    HermitianMatrixSpace()

    Use in the @variable macro to constrain a matrix of variables to be hermitian.

    Example

    julia> model = Model();
 
 julia> @variable(model, Q[1:2, 1:2] in HermitianMatrixSpace())
 2×2 LinearAlgebra.Hermitian{GenericAffExpr{ComplexF64, VariableRef}, Matrix{GenericAffExpr{ComplexF64, VariableRef}}}:
  real(Q[1,1])                    real(Q[1,2]) + imag(Q[1,2]) im
- real(Q[1,2]) - imag(Q[1,2]) im  real(Q[2,2])
    source

    HermitianPSDCone

    JuMP.HermitianPSDCone — Type
    HermitianPSDCone

    Hermitian positive semidefinite cone object that can be used to create a Hermitian positive semidefinite square matrix in the @variable and @constraint macros.

    Example

    Consider the following example:

    julia> model = Model();
+ real(Q[1,2]) - imag(Q[1,2]) im  real(Q[2,2])
    source

    HermitianPSDCone

    JuMP.HermitianPSDCone — Type
    HermitianPSDCone

    Hermitian positive semidefinite cone object that can be used to create a Hermitian positive semidefinite square matrix in the @variable and @constraint macros.

    Example

    Consider the following example:

    julia> model = Model();
 
 julia> @variable(model, H[1:3, 1:3] in HermitianPSDCone())
 3×3 LinearAlgebra.Hermitian{GenericAffExpr{ComplexF64, VariableRef}, Matrix{GenericAffExpr{ComplexF64, VariableRef}}}:
@@ -2814,18 +2814,18 @@
 
 julia> all_constraints(model, Vector{VariableRef}, MOI.HermitianPositiveSemidefiniteConeTriangle)
 1-element Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.VectorOfVariables, MathOptInterface.HermitianPositiveSemidefiniteConeTriangle}}}:
- [real(H[1,1]), real(H[1,2]), real(H[2,2]), real(H[1,3]), real(H[2,3]), real(H[3,3]), imag(H[1,2]), imag(H[1,3]), imag(H[2,3])] ∈ MathOptInterface.HermitianPositiveSemidefiniteConeTriangle(3)

    We see in the output of the last commands that 9 real variables were created. The matrix H constrains affine expressions in terms of these 9 variables that parametrize a Hermitian matrix.

    source

    IntegerRef

    JuMP.IntegerRef — Function
    IntegerRef(v::GenericVariableRef)

    Return a constraint reference to the constraint constraining v to be integer.

    Errors if one does not exist.

    See also is_integer, set_integer, unset_integer.

    Example

    julia> model = Model();
+ [real(H[1,1]), real(H[1,2]), real(H[2,2]), real(H[1,3]), real(H[2,3]), real(H[3,3]), imag(H[1,2]), imag(H[1,3]), imag(H[2,3])] ∈ MathOptInterface.HermitianPositiveSemidefiniteConeTriangle(3)

    We see in the output of the last commands that 9 real variables were created. The matrix H constrains affine expressions in terms of these 9 variables that parametrize a Hermitian matrix.

    source

    IntegerRef

    JuMP.IntegerRef — Function
    IntegerRef(v::GenericVariableRef)

    Return a constraint reference to the constraint constraining v to be integer.

    Errors if one does not exist.

    See also is_integer, set_integer, unset_integer.

    Example

    julia> model = Model();
 
 julia> @variable(model, x, Int);
 
 julia> IntegerRef(x)
-x integer
    source

    LPMatrixData

    LessThanZero

    JuMP.LessThanZero — Type
    GreaterThanZero()

    A struct used to intercept when <= or ≤ is used in a macro via operator_to_set.

    This struct is not the same as Nonpositives so that we can disambiguate x <= y and x - y in Nonpositives().

    This struct is not intended for general usage, but it may be useful to some JuMP extensions.

    Example

    julia> operator_to_set(error, Val(:<=))
-LessThanZero()
    source

    LinearTermIterator

    JuMP.LinearTermIterator — Type
    LinearTermIterator{GAE<:GenericAffExpr}

    A struct that implements the iterate protocol in order to iterate over tuples of (coefficient, variable) in the GenericAffExpr.

    source

    LowerBoundRef

    LPMatrixData

    LessThanZero

    JuMP.LessThanZero — Type
    GreaterThanZero()

    A struct used to intercept when <= or ≤ is used in a macro via operator_to_set.

    This struct is not the same as Nonpositives so that we can disambiguate x <= y and x - y in Nonpositives().

    This struct is not intended for general usage, but it may be useful to some JuMP extensions.

    Example

    julia> operator_to_set(error, Val(:<=))
+LessThanZero()
    source

    LinearTermIterator

    JuMP.LinearTermIterator — Type
    LinearTermIterator{GAE<:GenericAffExpr}

    A struct that implements the iterate protocol in order to iterate over tuples of (coefficient, variable) in the GenericAffExpr.

    source

    LowerBoundRef

    Model

    JuMP.Model — Type
    Model([optimizer_factory;] add_bridges::Bool = true)

    Create a new instance of a JuMP model.

    If optimizer_factory is provided, the model is initialized with thhe optimizer returned by MOI.instantiate(optimizer_factory).

    If optimizer_factory is not provided, use set_optimizer to set the optimizer before calling optimize!.

    If add_bridges, JuMP adds a MOI.Bridges.LazyBridgeOptimizer to automatically reformulate the problem into a form supported by the optimizer.

    Example

    julia> import Ipopt
+x ≥ 1
    source

    Model

    JuMP.Model — Type
    Model([optimizer_factory;] add_bridges::Bool = true)

    Create a new instance of a JuMP model.

    If optimizer_factory is provided, the model is initialized with thhe optimizer returned by MOI.instantiate(optimizer_factory).

    If optimizer_factory is not provided, use set_optimizer to set the optimizer before calling optimize!.

    If add_bridges, JuMP adds a MOI.Bridges.LazyBridgeOptimizer to automatically reformulate the problem into a form supported by the optimizer.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
@@ -2836,16 +2836,16 @@
 
 julia> import MultiObjectiveAlgorithms as MOA
 
-julia> model = Model(() -> MOA.Optimizer(HiGHS.Optimizer); add_bridges = false);
    source

    ModelMode

    JuMP.ModelMode — Type
    ModelMode

    An enum to describe the state of the CachingOptimizer inside a JuMP model.

    See also: mode.

    Values

    Possible values are:

    • [AUTOMATIC]: moi_backend field holds a CachingOptimizer in AUTOMATIC mode.
    • [MANUAL]: moi_backend field holds a CachingOptimizer in MANUAL mode.
    • [DIRECT]: moi_backend field holds an AbstractOptimizer. No extra copy of the model is stored. The moi_backend must support add_constraint etc.
    source

    NLPEvaluator

    JuMP.NLPEvaluator — Function
    NLPEvaluator(
+julia> model = Model(() -> MOA.Optimizer(HiGHS.Optimizer); add_bridges = false);
    source

    ModelMode

    JuMP.ModelMode — Type
    ModelMode

    An enum to describe the state of the CachingOptimizer inside a JuMP model.

    See also: mode.

    Values

    Possible values are:

    • [AUTOMATIC]: moi_backend field holds a CachingOptimizer in AUTOMATIC mode.
    • [MANUAL]: moi_backend field holds a CachingOptimizer in MANUAL mode.
    • [DIRECT]: moi_backend field holds an AbstractOptimizer. No extra copy of the model is stored. The moi_backend must support add_constraint etc.
    source

    NLPEvaluator

    JuMP.NLPEvaluator — Function
    NLPEvaluator(
     model::Model,
     _differentiation_backend::MOI.Nonlinear.AbstractAutomaticDifferentiation =
         MOI.Nonlinear.SparseReverseMode(),
-)

    Return an MOI.AbstractNLPEvaluator constructed from model

    Warning

    Before using, you must initialize the evaluator using MOI.initialize.

    Experimental

    These features may change or be removed in any future version of JuMP.

    Pass _differentiation_backend to specify the differentiation backend used to compute derivatives.

    source

    NoOptimizer

    JuMP.NoOptimizer — Type
    struct NoOptimizer <: Exception end

    An error thrown when no optimizer is set and one is required.

    The optimizer can be provided to the Model constructor or by calling set_optimizer.

    Example

    julia> model = Model();
+)

    Return an MOI.AbstractNLPEvaluator constructed from model

    Warning

    Before using, you must initialize the evaluator using MOI.initialize.

    Experimental

    These features may change or be removed in any future version of JuMP.

    Pass _differentiation_backend to specify the differentiation backend used to compute derivatives.

    source

    NoOptimizer

    JuMP.NoOptimizer — Type
    struct NoOptimizer <: Exception end

    An error thrown when no optimizer is set and one is required.

    The optimizer can be provided to the Model constructor or by calling set_optimizer.

    Example

    julia> model = Model();
 
 julia> optimize!(model)
 ERROR: NoOptimizer()
 Stacktrace:
-[...]
    source

    NonlinearExpr

    NonlinearOperator

    JuMP.NonlinearOperator — Type
    NonlinearOperator(func::Function, head::Symbol)

    A callable struct (functor) representing a function named head.

    When called with AbstractJuMPScalars, the struct returns a GenericNonlinearExpr.

    When called with non-JuMP types, the struct returns the evaluation of func(args...).

    Unless head is special-cased by the optimizer, the operator must have already been added to the model using add_nonlinear_operator or @operator.

    Example

    julia> model = Model();
+[...]
    source

    NonlinearExpr

    NonlinearOperator

    JuMP.NonlinearOperator — Type
    NonlinearOperator(func::Function, head::Symbol)

    A callable struct (functor) representing a function named head.

    When called with AbstractJuMPScalars, the struct returns a GenericNonlinearExpr.

    When called with non-JuMP types, the struct returns the evaluation of func(args...).

    Unless head is special-cased by the optimizer, the operator must have already been added to the model using add_nonlinear_operator or @operator.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -2869,7 +2869,7 @@
 op_f(x)
 
 julia> bar(2.0)
-4.0
    source

    Nonnegatives

    JuMP.Nonnegatives — Type
    Nonnegatives()

    The JuMP equivalent of the MOI.Nonnegatives set, in which the dimension is inferred from the corresponding function.

    Example

    julia> model = Model();
+4.0
    source

    Nonnegatives

    JuMP.Nonnegatives — Type
    Nonnegatives()

    The JuMP equivalent of the MOI.Nonnegatives set, in which the dimension is inferred from the corresponding function.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2])
 2-element Vector{VariableRef}:
@@ -2884,7 +2884,7 @@
 julia> b = [5, 6];
 
 julia> @constraint(model, A * x >= b)
-[x[1] + 2 x[2] - 5, 3 x[1] + 4 x[2] - 6] ∈ Nonnegatives()
    source

    Nonpositives

    JuMP.Nonpositives — Type
    Nonpositives()

    The JuMP equivalent of the MOI.Nonpositives set, in which the dimension is inferred from the corresponding function.

    Example

    julia> model = Model();
+[x[1] + 2 x[2] - 5, 3 x[1] + 4 x[2] - 6] ∈ Nonnegatives()
    source

    Nonpositives

    JuMP.Nonpositives — Type
    Nonpositives()

    The JuMP equivalent of the MOI.Nonpositives set, in which the dimension is inferred from the corresponding function.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2])
 2-element Vector{VariableRef}:
@@ -2899,14 +2899,14 @@
 julia> b = [5, 6];
 
 julia> @constraint(model, A * x <= b)
-[x[1] + 2 x[2] - 5, 3 x[1] + 4 x[2] - 6] ∈ Nonpositives()
    source

    OptimizationSense

    OptimizeNotCalled

    JuMP.OptimizeNotCalled — Type
    struct OptimizeNotCalled <: Exception end

    An error thrown when a result attribute cannot be queried before optimize! is called.

    Example

    julia> import Ipopt
+[x[1] + 2 x[2] - 5, 3 x[1] + 4 x[2] - 6] ∈ Nonpositives()
    source

    OptimizationSense

    OptimizeNotCalled

    JuMP.OptimizeNotCalled — Type
    struct OptimizeNotCalled <: Exception end

    An error thrown when a result attribute cannot be queried before optimize! is called.

    Example

    julia> import Ipopt
 
 julia> model = Model(Ipopt.Optimizer);
 
 julia> objective_value(model)
 ERROR: OptimizeNotCalled()
 Stacktrace:
-[...]
    source

    PSDCone

    JuMP.PSDCone — Type
    PSDCone

    Positive semidefinite cone object that can be used to constrain a square matrix to be positive semidefinite in the @constraint macro.

    If the matrix has type Symmetric then the columns vectorization (the vector obtained by concatenating the columns) of its upper triangular part is constrained to belong to the MOI.PositiveSemidefiniteConeTriangle set, otherwise its column vectorization is constrained to belong to the MOI.PositiveSemidefiniteConeSquare set.

    Example

    Non-symmetric case:

    julia> model = Model();
+[...]
    source

    PSDCone

    JuMP.PSDCone — Type
    PSDCone

    Positive semidefinite cone object that can be used to constrain a square matrix to be positive semidefinite in the @constraint macro.

    If the matrix has type Symmetric then the columns vectorization (the vector obtained by concatenating the columns) of its upper triangular part is constrained to belong to the MOI.PositiveSemidefiniteConeTriangle set, otherwise its column vectorization is constrained to belong to the MOI.PositiveSemidefiniteConeSquare set.

    Example

    Non-symmetric case:

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -2947,7 +2947,7 @@
  x - 4
 
 julia> moi_set(constraint_object(cref))
-MathOptInterface.PositiveSemidefiniteConeTriangle(2)
    source

    Parameter

    JuMP.Parameter — Type
    Parameter(value)

    A short-cut for the MOI.Parameter set.

    Example

    julia> model = Model();
+MathOptInterface.PositiveSemidefiniteConeTriangle(2)
    source

    Parameter

    JuMP.Parameter — Type
    Parameter(value)

    A short-cut for the MOI.Parameter set.

    Example

    julia> model = Model();
 
 julia> @variable(model, x in Parameter(2))
 x
@@ -2955,7 +2955,7 @@
 julia> print(model)
 Feasibility
 Subject to
- x ∈ MathOptInterface.Parameter{Float64}(2.0)
    source

    ParameterRef

    ParameterRef

    JuMP.ParameterRef — Function
    ParameterRef(x::GenericVariableRef)

    Return a constraint reference to the constraint constraining x to be a parameter.

    Errors if one does not exist.

    See also is_parameter, set_parameter_value, parameter_value.

    Example

    julia> model = Model();
 
 julia> @variable(model, p in Parameter(2))
 p
@@ -2968,7 +2968,7 @@
 julia> ParameterRef(x)
 ERROR: Variable x is not a parameter.
 Stacktrace:
-[...]
    source

    QuadExpr

    QuadTermIterator

    JuMP.QuadTermIterator — Type
    QuadTermIterator{GQE<:GenericQuadExpr}

    A struct that implements the iterate protocol in order to iterate over tuples of (coefficient, variable, variable) in the GenericQuadExpr.

    source

    ReferenceMap

    JuMP.ReferenceMap — Type
    GenericReferenceMap{T}

    Mapping between variable and constraint reference of a model and its copy. The reference of the copied model can be obtained by indexing the map with the reference of the corresponding reference of the original model.

    source

    ResultStatusCode

    JuMP.ResultStatusCode — Type
    ResultStatusCode

    An Enum of possible values for the PrimalStatus and DualStatus attributes.

    The values indicate how to interpret the result vector.

    Values

    Possible values are:

    • NO_SOLUTION: the result vector is empty.
    • FEASIBLE_POINT: the result vector is a feasible point.
    • NEARLY_FEASIBLE_POINT: the result vector is feasible if some constraint tolerances are relaxed.
    • INFEASIBLE_POINT: the result vector is an infeasible point.
    • INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.
    • NEARLY_INFEASIBILITY_CERTIFICATE: the result satisfies a relaxed criterion for a certificate of infeasibility.
    • REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.
    • NEARLY_REDUCTION_CERTIFICATE: the result satisfies a relaxed criterion for an ill-posed certificate.
    • UNKNOWN_RESULT_STATUS: the result vector contains a solution with an unknown interpretation.
    • OTHER_RESULT_STATUS: the result vector contains a solution with an interpretation not covered by one of the statuses defined above
    source

    RotatedSecondOrderCone

    JuMP.RotatedSecondOrderCone — Type
    RotatedSecondOrderCone

    Rotated second order cone object that can be used to constrain the square of the euclidean norm of a vector x to be less than or equal to $2tu$ where t and u are nonnegative scalars. This is a shortcut for the MOI.RotatedSecondOrderCone.

    Example

    The following constrains $\|(x-1, x-2)\|^2_2 \le 2tx$ and $t, x \ge 0$:

    julia> model = Model();
+[...]
    source

    QuadExpr

    QuadTermIterator

    JuMP.QuadTermIterator — Type
    QuadTermIterator{GQE<:GenericQuadExpr}

    A struct that implements the iterate protocol in order to iterate over tuples of (coefficient, variable, variable) in the GenericQuadExpr.

    source

    ReferenceMap

    JuMP.ReferenceMap — Type
    GenericReferenceMap{T}

    Mapping between variable and constraint reference of a model and its copy. The reference of the copied model can be obtained by indexing the map with the reference of the corresponding reference of the original model.

    source

    ResultStatusCode

    JuMP.ResultStatusCode — Type
    ResultStatusCode

    An Enum of possible values for the PrimalStatus and DualStatus attributes.

    The values indicate how to interpret the result vector.

    Values

    Possible values are:

    • NO_SOLUTION: the result vector is empty.
    • FEASIBLE_POINT: the result vector is a feasible point.
    • NEARLY_FEASIBLE_POINT: the result vector is feasible if some constraint tolerances are relaxed.
    • INFEASIBLE_POINT: the result vector is an infeasible point.
    • INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.
    • NEARLY_INFEASIBILITY_CERTIFICATE: the result satisfies a relaxed criterion for a certificate of infeasibility.
    • REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.
    • NEARLY_REDUCTION_CERTIFICATE: the result satisfies a relaxed criterion for an ill-posed certificate.
    • UNKNOWN_RESULT_STATUS: the result vector contains a solution with an unknown interpretation.
    • OTHER_RESULT_STATUS: the result vector contains a solution with an interpretation not covered by one of the statuses defined above
    source

    RotatedSecondOrderCone

    JuMP.RotatedSecondOrderCone — Type
    RotatedSecondOrderCone

    Rotated second order cone object that can be used to constrain the square of the euclidean norm of a vector x to be less than or equal to $2tu$ where t and u are nonnegative scalars. This is a shortcut for the MOI.RotatedSecondOrderCone.

    Example

    The following constrains $\|(x-1, x-2)\|^2_2 \le 2tx$ and $t, x \ge 0$:

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -2977,7 +2977,7 @@
 t
 
 julia> @constraint(model, [t, x, x-1, x-2] in RotatedSecondOrderCone())
-[t, x, x - 1, x - 2] ∈ MathOptInterface.RotatedSecondOrderCone(4)
    source

    SOS1

    JuMP.SOS1 — Type
    SOS1(weights = Real[])

    The SOS1 (Special Ordered Set of Type 1) set constrains a vector x to the set where at most one variable can take a non-zero value, and all other elements are zero.

    The weights vector, if specified, induces an ordering of the variables; as such, it should contain unique values. The weights vector must have the same number of elements as the vector x, and the element weights[i] corresponds to element x[i]. If not provided, the weights vector defaults to weights[i] = i.

    This is a shortcut for the MOI.SOS1 set.

    Example

    julia> model = Model();
+[t, x, x - 1, x - 2] ∈ MathOptInterface.RotatedSecondOrderCone(4)
    source

    SOS1

    JuMP.SOS1 — Type
    SOS1(weights = Real[])

    The SOS1 (Special Ordered Set of Type 1) set constrains a vector x to the set where at most one variable can take a non-zero value, and all other elements are zero.

    The weights vector, if specified, induces an ordering of the variables; as such, it should contain unique values. The weights vector must have the same number of elements as the vector x, and the element weights[i] corresponds to element x[i]. If not provided, the weights vector defaults to weights[i] = i.

    This is a shortcut for the MOI.SOS1 set.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:3] in SOS1([4.1, 3.2, 5.0]))
 3-element Vector{VariableRef}:
@@ -2988,7 +2988,7 @@
 julia> print(model)
 Feasibility
 Subject to
- [x[1], x[2], x[3]] ∈ MathOptInterface.SOS1{Float64}([4.1, 3.2, 5.0])
    source

    SOS2

    JuMP.SOS2 — Type
    SOS2(weights = Real[])

    The SOS2 (Special Ordered Set of Type 2) set constrains a vector x to the set where at most two variables can take a non-zero value, and all other elements are zero. In addition, the two non-zero values must be consecutive given the ordering of the x vector induced by weights.

    The weights vector, if specified, induces an ordering of the variables; as such, it must contain unique values. The weights vector must have the same number of elements as the vector x, and the element weights[i] corresponds to element x[i]. If not provided, the weights vector defaults to weights[i] = i.

    This is a shortcut for the MOI.SOS2 set.

    Example

    julia> model = Model();
+ [x[1], x[2], x[3]] ∈ MathOptInterface.SOS1{Float64}([4.1, 3.2, 5.0])
    source

    SOS2

    JuMP.SOS2 — Type
    SOS2(weights = Real[])

    The SOS2 (Special Ordered Set of Type 2) set constrains a vector x to the set where at most two variables can take a non-zero value, and all other elements are zero. In addition, the two non-zero values must be consecutive given the ordering of the x vector induced by weights.

    The weights vector, if specified, induces an ordering of the variables; as such, it must contain unique values. The weights vector must have the same number of elements as the vector x, and the element weights[i] corresponds to element x[i]. If not provided, the weights vector defaults to weights[i] = i.

    This is a shortcut for the MOI.SOS2 set.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:3] in SOS2([4.1, 3.2, 5.0]))
 3-element Vector{VariableRef}:
@@ -2999,7 +2999,7 @@
 julia> print(model)
 Feasibility
 Subject to
- [x[1], x[2], x[3]] ∈ MathOptInterface.SOS2{Float64}([4.1, 3.2, 5.0])
    source

    ScalarConstraint

    JuMP.ScalarConstraint — Type
    struct ScalarConstraint

    The data for a scalar constraint.

    See also the documentation on JuMP's representation of constraints for more background.

    Fields

    • .func: field contains a JuMP object representing the function
    • .set: field contains the MOI set

    Example

    A scalar constraint:

    julia> model = Model();
+ [x[1], x[2], x[3]] ∈ MathOptInterface.SOS2{Float64}([4.1, 3.2, 5.0])
    source

    ScalarConstraint

    JuMP.ScalarConstraint — Type
    struct ScalarConstraint

    The data for a scalar constraint.

    See also the documentation on JuMP's representation of constraints for more background.

    Fields

    • .func: field contains a JuMP object representing the function
    • .set: field contains the MOI set

    Example

    A scalar constraint:

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3016,14 +3016,14 @@
 2 x
 
 julia> object.set
-MathOptInterface.LessThan{Float64}(1.0)
    source

    ScalarShape

    ScalarShape

    JuMP.ScalarShape — Type
    ScalarShape()

    An AbstractShape that represents scalar constraints.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
 julia> c = @constraint(model, x[2] <= 1);
 
 julia> shape(constraint_object(c))
-ScalarShape()
    source

    ScalarVariable

    SecondOrderCone

    JuMP.SecondOrderCone — Type
    SecondOrderCone

    Second order cone object that can be used to constrain the euclidean norm of a vector x to be less than or equal to a nonnegative scalar t. This is a shortcut for the MOI.SecondOrderCone.

    Example

    The following constrains $\|(x-1, x-2)\|_2 \le t$ and $t \ge 0$:

    julia> model = Model();
+ScalarShape()
    source

    ScalarVariable

    SecondOrderCone

    JuMP.SecondOrderCone — Type
    SecondOrderCone

    Second order cone object that can be used to constrain the euclidean norm of a vector x to be less than or equal to a nonnegative scalar t. This is a shortcut for the MOI.SecondOrderCone.

    Example

    The following constrains $\|(x-1, x-2)\|_2 \le t$ and $t \ge 0$:

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -3032,7 +3032,7 @@
 t
 
 julia> @constraint(model, [t, x-1, x-2] in SecondOrderCone())
-[t, x - 1, x - 2] ∈ MathOptInterface.SecondOrderCone(3)
    source

    Semicontinuous

    JuMP.Semicontinuous — Type
    Semicontinuous(lower, upper)

    A short-cut for the MOI.Semicontinuous set.

    This short-cut is useful because it automatically promotes lower and upper to the same type, and converts them into the element type supported by the JuMP model.

    Example

    julia> model = Model();
+[t, x - 1, x - 2] ∈ MathOptInterface.SecondOrderCone(3)
    source

    Semicontinuous

    JuMP.Semicontinuous — Type
    Semicontinuous(lower, upper)

    A short-cut for the MOI.Semicontinuous set.

    This short-cut is useful because it automatically promotes lower and upper to the same type, and converts them into the element type supported by the JuMP model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x in Semicontinuous(1, 2))
 x
@@ -3040,7 +3040,7 @@
 julia> print(model)
 Feasibility
 Subject to
- x ∈ MathOptInterface.Semicontinuous{Int64}(1, 2)
    source

    Semiinteger

    JuMP.Semiinteger — Type
    Semiinteger(lower, upper)

    A short-cut for the MOI.Semiinteger set.

    This short-cut is useful because it automatically promotes lower and upper to the same type, and converts them into the element type supported by the JuMP model.

    Example

    julia> model = Model();
+ x ∈ MathOptInterface.Semicontinuous{Int64}(1, 2)
    source

    Semiinteger

    JuMP.Semiinteger — Type
    Semiinteger(lower, upper)

    A short-cut for the MOI.Semiinteger set.

    This short-cut is useful because it automatically promotes lower and upper to the same type, and converts them into the element type supported by the JuMP model.

    Example

    julia> model = Model();
 
 julia> @variable(model, x in Semiinteger(3, 5))
 x
@@ -3048,12 +3048,12 @@
 julia> print(model)
 Feasibility
 Subject to
- x ∈ MathOptInterface.Semiinteger{Int64}(3, 5)
    source

    SensitivityReport

    SkewSymmetricMatrixShape

    JuMP.SkewSymmetricMatrixShape — Type
    SkewSymmetricMatrixShape

    Shape object for a skew symmetric square matrix of side_dimension rows and columns. The vectorized form contains the entries of the upper-right triangular part of the matrix (without the diagonal) given column by column (or equivalently, the entries of the lower-left triangular part given row by row). The diagonal is zero.

    source

    SkewSymmetricMatrixSpace

    JuMP.SkewSymmetricMatrixSpace — Type
    SkewSymmetricMatrixSpace()

    Use in the @variable macro to constrain a matrix of variables to be skew-symmetric.

    Example

    julia> model = Model();
+ x ∈ MathOptInterface.Semiinteger{Int64}(3, 5)
    source

    SensitivityReport

    SkewSymmetricMatrixShape

    JuMP.SkewSymmetricMatrixShape — Type
    SkewSymmetricMatrixShape

    Shape object for a skew symmetric square matrix of side_dimension rows and columns. The vectorized form contains the entries of the upper-right triangular part of the matrix (without the diagonal) given column by column (or equivalently, the entries of the lower-left triangular part given row by row). The diagonal is zero.

    source

    SkewSymmetricMatrixSpace

    JuMP.SkewSymmetricMatrixSpace — Type
    SkewSymmetricMatrixSpace()

    Use in the @variable macro to constrain a matrix of variables to be skew-symmetric.

    Example

    julia> model = Model();
 
 julia> @variable(model, Q[1:2, 1:2] in SkewSymmetricMatrixSpace())
 2×2 Matrix{AffExpr}:
  0        Q[1,2]
- -Q[1,2]  0
    source

    SkipModelConvertScalarSetWrapper

    JuMP.SkipModelConvertScalarSetWrapper — Type
    SkipModelConvertScalarSetWrapper(set::MOI.AbstractScalarSet)

    JuMP uses model_convert to automatically promote MOI.AbstractScalarSet sets to the same value_type as the model.

    In cases there this is undesirable, wrap the set in SkipModelConvertScalarSetWrapper to pass the set un-changed to the solver.

    Warning

    This struct is intended for use internally by JuMP extensions. You should not need to use it in regular JuMP code.

    Example

    julia> model = Model();
+ -Q[1,2]  0
    source

    SkipModelConvertScalarSetWrapper

    JuMP.SkipModelConvertScalarSetWrapper — Type
    SkipModelConvertScalarSetWrapper(set::MOI.AbstractScalarSet)

    JuMP uses model_convert to automatically promote MOI.AbstractScalarSet sets to the same value_type as the model.

    In cases there this is undesirable, wrap the set in SkipModelConvertScalarSetWrapper to pass the set un-changed to the solver.

    Warning

    This struct is intended for use internally by JuMP extensions. You should not need to use it in regular JuMP code.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3061,15 +3061,15 @@
 x = 0.5
 
 julia> @constraint(model, x in SkipModelConvertScalarSetWrapper(MOI.EqualTo(1 // 2)))
-x = 1//2
    source

    SquareMatrixShape

    JuMP.SquareMatrixShape — Type
    SquareMatrixShape

    Shape object for a square matrix of side_dimension rows and columns. The vectorized form contains the entries of the matrix given column by column (or equivalently, the entries of the lower-left triangular part given row by row).

    source

    SymmetricMatrixAdjointShape

    SymmetricMatrixShape

    SquareMatrixShape

    JuMP.SquareMatrixShape — Type
    SquareMatrixShape

    Shape object for a square matrix of side_dimension rows and columns. The vectorized form contains the entries of the matrix given column by column (or equivalently, the entries of the lower-left triangular part given row by row).

    source

    SymmetricMatrixAdjointShape

    SymmetricMatrixShape

    JuMP.SymmetricMatrixShape — Type
    SymmetricMatrixShape(
     side_dimension::Int;
     needs_adjoint_dual::Bool = false,
-)

    The shape object for a symmetric square matrix of side_dimension rows and columns.

    The vectorized form contains the entries of the upper-right triangular part of the matrix given column by column (or equivalently, the entries of the lower-left triangular part given row by row).

    needs_adjoint_dual

    By default, the dual_shape of SymmetricMatrixShape is also SymmetricMatrixShape. This is true for cases such as a LinearAlgebra.Symmetric matrix in PSDCone.

    However, JuMP also supports LinearAlgebra.Symmetric matrix in Zeros, which is interpreted as an element-wise equality constraint. By exploiting symmetry, we pass only the upper triangle of the equality constraints. This works for the primal, but it leads to a factor of 2 difference in the off-diagonal dual elements. (The dual value of the (i, j) element in the triangle formulation should be divided by 2 when spread across the (i, j) and (j, i) elements in the square matrix formulation.) If the constraint has this dual inconsistency, set needs_adjoint_dual = true.

    source

    SymmetricMatrixSpace

    JuMP.SymmetricMatrixSpace — Type
    SymmetricMatrixSpace()

    Use in the @variable macro to constrain a matrix of variables to be symmetric.

    Example

    julia> model = Model();
+)

    The shape object for a symmetric square matrix of side_dimension rows and columns.

    The vectorized form contains the entries of the upper-right triangular part of the matrix given column by column (or equivalently, the entries of the lower-left triangular part given row by row).

    needs_adjoint_dual

    By default, the dual_shape of SymmetricMatrixShape is also SymmetricMatrixShape. This is true for cases such as a LinearAlgebra.Symmetric matrix in PSDCone.

    However, JuMP also supports LinearAlgebra.Symmetric matrix in Zeros, which is interpreted as an element-wise equality constraint. By exploiting symmetry, we pass only the upper triangle of the equality constraints. This works for the primal, but it leads to a factor of 2 difference in the off-diagonal dual elements. (The dual value of the (i, j) element in the triangle formulation should be divided by 2 when spread across the (i, j) and (j, i) elements in the square matrix formulation.) If the constraint has this dual inconsistency, set needs_adjoint_dual = true.

    source

    SymmetricMatrixSpace

    JuMP.SymmetricMatrixSpace — Type
    SymmetricMatrixSpace()

    Use in the @variable macro to constrain a matrix of variables to be symmetric.

    Example

    julia> model = Model();
 
 julia> @variable(model, Q[1:2, 1:2] in SymmetricMatrixSpace())
 2×2 LinearAlgebra.Symmetric{VariableRef, Matrix{VariableRef}}:
  Q[1,1]  Q[1,2]
- Q[1,2]  Q[2,2]
    source

    TerminationStatusCode

    JuMP.TerminationStatusCode — Type
    TerminationStatusCode

    An Enum of possible values for the TerminationStatus attribute. This attribute is meant to explain the reason why the optimizer stopped executing in the most recent call to optimize!.

    Values

    Possible values are:

    • OPTIMIZE_NOT_CALLED: The algorithm has not started.
    • OPTIMAL: The algorithm found a globally optimal solution.
    • INFEASIBLE: The algorithm concluded that no feasible solution exists.
    • DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.
    • LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.
    • LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.
    • INFEASIBLE_OR_UNBOUNDED: The algorithm stopped because it decided that the problem is infeasible or unbounded; this occasionally happens during MIP presolve.
    • ALMOST_OPTIMAL: The algorithm found a globally optimal solution to relaxed tolerances.
    • ALMOST_INFEASIBLE: The algorithm concluded that no feasible solution exists within relaxed tolerances.
    • ALMOST_DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem within relaxed tolerances.
    • ALMOST_LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, or could not find directions for improvement within relaxed tolerances.
    • ITERATION_LIMIT: An iterative algorithm stopped after conducting the maximum number of iterations.
    • TIME_LIMIT: The algorithm stopped after a user-specified computation time.
    • NODE_LIMIT: A branch-and-bound algorithm stopped because it explored a maximum number of nodes in the branch-and-bound tree.
    • SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.
    • MEMORY_LIMIT: The algorithm stopped because it ran out of memory.
    • OBJECTIVE_LIMIT: The algorithm stopped because it found a solution better than a minimum limit set by the user.
    • NORM_LIMIT: The algorithm stopped because the norm of an iterate became too large.
    • OTHER_LIMIT: The algorithm stopped due to a limit not covered by one of the _LIMIT_ statuses above.
    • SLOW_PROGRESS: The algorithm stopped because it was unable to continue making progress towards the solution.
    • NUMERICAL_ERROR: The algorithm stopped because it encountered unrecoverable numerical error.
    • INVALID_MODEL: The algorithm stopped because the model is invalid.
    • INVALID_OPTION: The algorithm stopped because it was provided an invalid option.
    • INTERRUPTED: The algorithm stopped because of an interrupt signal.
    • OTHER_ERROR: The algorithm stopped because of an error not covered by one of the statuses defined above.
    source

    UnorderedPair

    TerminationStatusCode

    JuMP.TerminationStatusCode — Type
    TerminationStatusCode

    An Enum of possible values for the TerminationStatus attribute. This attribute is meant to explain the reason why the optimizer stopped executing in the most recent call to optimize!.

    Values

    Possible values are:

    • OPTIMIZE_NOT_CALLED: The algorithm has not started.
    • OPTIMAL: The algorithm found a globally optimal solution.
    • INFEASIBLE: The algorithm concluded that no feasible solution exists.
    • DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.
    • LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.
    • LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.
    • INFEASIBLE_OR_UNBOUNDED: The algorithm stopped because it decided that the problem is infeasible or unbounded; this occasionally happens during MIP presolve.
    • ALMOST_OPTIMAL: The algorithm found a globally optimal solution to relaxed tolerances.
    • ALMOST_INFEASIBLE: The algorithm concluded that no feasible solution exists within relaxed tolerances.
    • ALMOST_DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem within relaxed tolerances.
    • ALMOST_LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, or could not find directions for improvement within relaxed tolerances.
    • ITERATION_LIMIT: An iterative algorithm stopped after conducting the maximum number of iterations.
    • TIME_LIMIT: The algorithm stopped after a user-specified computation time.
    • NODE_LIMIT: A branch-and-bound algorithm stopped because it explored a maximum number of nodes in the branch-and-bound tree.
    • SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.
    • MEMORY_LIMIT: The algorithm stopped because it ran out of memory.
    • OBJECTIVE_LIMIT: The algorithm stopped because it found a solution better than a minimum limit set by the user.
    • NORM_LIMIT: The algorithm stopped because the norm of an iterate became too large.
    • OTHER_LIMIT: The algorithm stopped due to a limit not covered by one of the _LIMIT_ statuses above.
    • SLOW_PROGRESS: The algorithm stopped because it was unable to continue making progress towards the solution.
    • NUMERICAL_ERROR: The algorithm stopped because it encountered unrecoverable numerical error.
    • INVALID_MODEL: The algorithm stopped because the model is invalid.
    • INVALID_OPTION: The algorithm stopped because it was provided an invalid option.
    • INTERRUPTED: The algorithm stopped because of an interrupt signal.
    • OTHER_ERROR: The algorithm stopped because of an error not covered by one of the statuses defined above.
    source

    UnorderedPair

    JuMP.UnorderedPair — Type
    UnorderedPair(a::T, b::T)

    A wrapper type used by GenericQuadExpr with fields .a and .b.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -3078,12 +3078,12 @@
 
 julia> expr.terms
 OrderedCollections.OrderedDict{UnorderedPair{VariableRef}, Float64} with 1 entry:
-  UnorderedPair{VariableRef}(x[1], x[2]) => 2.0
    source

    UpperBoundRef

    UpperBoundRef

    VariableConstrainedOnCreation

    JuMP.VariableConstrainedOnCreation — Type
    VariableConstrainedOnCreation <: AbstractVariable

    Variable scalar_variables constrained to belong to set.

    Adding this variable can be understood as doing:

    function JuMP.add_variable(
+x ≤ 1
    source

    VariableConstrainedOnCreation

    JuMP.VariableConstrainedOnCreation — Type
    VariableConstrainedOnCreation <: AbstractVariable

    Variable scalar_variables constrained to belong to set.

    Adding this variable can be understood as doing:

    function JuMP.add_variable(
     model::GenericModel,
     variable::VariableConstrainedOnCreation,
     names,
@@ -3091,9 +3091,9 @@
     var_ref = add_variable(model, variable.scalar_variable, name)
     add_constraint(model, VectorConstraint(var_ref, variable.set))
     return var_ref
-end

    but adds the variables with MOI.add_constrained_variable(model, variable.set) instead.

    source

    VariableInfo

    JuMP.VariableInfo — Type
    VariableInfo{S,T,U,V}

    A struct by JuMP internally when creating variables. This may also be used by JuMP extensions to create new types of variables.

    See also: ScalarVariable.

    source

    VariableNotOwned

    JuMP.VariableNotOwned — Type
    struct VariableNotOwned{V<:AbstractVariableRef} <: Exception
+end

    but adds the variables with MOI.add_constrained_variable(model, variable.set) instead.

    source

    VariableInfo

    JuMP.VariableInfo — Type
    VariableInfo{S,T,U,V}

    A struct by JuMP internally when creating variables. This may also be used by JuMP extensions to create new types of variables.

    See also: ScalarVariable.

    source

    VariableNotOwned

    JuMP.VariableNotOwned — Type
    struct VariableNotOwned{V<:AbstractVariableRef} <: Exception
     variable::V
-end

    The variable variable was used in a model different to owner_model(variable).

    source

    VariableRef

    JuMP.VariableRef — Type
    GenericVariableRef{T} <: AbstractVariableRef

    Holds a reference to the model and the corresponding MOI.VariableIndex.

    source

    VariablesConstrainedOnCreation

    JuMP.VariablesConstrainedOnCreation — Type
    VariablesConstrainedOnCreation <: AbstractVariable

    Vector of variables scalar_variables constrained to belong to set. Adding this variable can be thought as doing:

    function JuMP.add_variable(
+end

    The variable variable was used in a model different to owner_model(variable).

    source

    VariableRef

    JuMP.VariableRef — Type
    GenericVariableRef{T} <: AbstractVariableRef

    Holds a reference to the model and the corresponding MOI.VariableIndex.

    source

    VariablesConstrainedOnCreation

    JuMP.VariablesConstrainedOnCreation — Type
    VariablesConstrainedOnCreation <: AbstractVariable

    Vector of variables scalar_variables constrained to belong to set. Adding this variable can be thought as doing:

    function JuMP.add_variable(
     model::GenericModel,
     variable::VariablesConstrainedOnCreation,
     names,
@@ -3102,7 +3102,7 @@
     var_refs = add_variable.(model, variable.scalar_variables, v_names)
     add_constraint(model, VectorConstraint(var_refs, variable.set))
     return reshape_vector(var_refs, variable.shape)
-end

    but adds the variables with MOI.add_constrained_variables(model, variable.set) instead. See the MOI documentation for the difference between adding the variables with MOI.add_constrained_variables and adding them with MOI.add_variables and adding the constraint separately.

    source

    VectorConstraint

    JuMP.VectorConstraint — Type
    struct VectorConstraint

    The data for a vector constraint.

    See also the documentation on JuMP's representation of constraints.

    Fields

    • func: field contains a JuMP object representing the function
    • set: field contains the MOI set.
    • shape: field contains an AbstractShape matching the form in which the constraint was constructed (for example, by using matrices or flat vectors).

    Example

    julia> model = Model();
+end

    but adds the variables with MOI.add_constrained_variables(model, variable.set) instead. See the MOI documentation for the difference between adding the variables with MOI.add_constrained_variables and adding them with MOI.add_variables and adding the constraint separately.

    source

    VectorConstraint

    JuMP.VectorConstraint — Type
    struct VectorConstraint

    The data for a vector constraint.

    See also the documentation on JuMP's representation of constraints.

    Fields

    • func: field contains a JuMP object representing the function
    • set: field contains the MOI set.
    • shape: field contains an AbstractShape matching the form in which the constraint was constructed (for example, by using matrices or flat vectors).

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:3]);
 
@@ -3125,14 +3125,14 @@
 MathOptInterface.SecondOrderCone(3)
 
 julia> object.shape
-VectorShape()
    source

    VectorShape

    VectorShape

    JuMP.VectorShape — Type
    VectorShape()

    An AbstractShape that represents vector-valued constraints.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
 julia> c = @constraint(model, x in SOS1());
 
 julia> shape(constraint_object(c))
-VectorShape()
    source

    Zeros

    JuMP.Zeros — Type
    Zeros()

    The JuMP equivalent of the MOI.Zeros set, in which the dimension is inferred from the corresponding function.

    Example

    julia> model = Model();
+VectorShape()
    source

    Zeros

    JuMP.Zeros — Type
    Zeros()

    The JuMP equivalent of the MOI.Zeros set, in which the dimension is inferred from the corresponding function.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2])
 2-element Vector{VariableRef}:
@@ -3147,7 +3147,7 @@
 julia> b = [5, 6];
 
 julia> @constraint(model, A * x == b)
-[x[1] + 2 x[2] - 5, 3 x[1] + 4 x[2] - 6] ∈ Zeros()
    source

    ALMOST_DUAL_INFEASIBLE

    ALMOST_INFEASIBLE

    ALMOST_LOCALLY_SOLVED

    JuMP.ALMOST_LOCALLY_SOLVED — Constant
    ALMOST_LOCALLY_SOLVED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    ALMOST_LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, or could not find directions for improvement within relaxed tolerances.

    source

    ALMOST_OPTIMAL

    AUTOMATIC

    DIRECT

    JuMP.DIRECT — Constant

    moi_backend field holds an AbstractOptimizer. No extra copy of the model is stored. The moi_backend must support add_constraint etc.

    source

    DUAL_INFEASIBLE

    JuMP.DUAL_INFEASIBLE — Constant
    DUAL_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.

    source

    FEASIBILITY_SENSE

    FEASIBLE_POINT

    INFEASIBILITY_CERTIFICATE

    JuMP.INFEASIBILITY_CERTIFICATE — Constant
    INFEASIBILITY_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.

    source

    INFEASIBLE

    INFEASIBLE_OR_UNBOUNDED

    JuMP.INFEASIBLE_OR_UNBOUNDED — Constant
    INFEASIBLE_OR_UNBOUNDED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    INFEASIBLE_OR_UNBOUNDED: The algorithm stopped because it decided that the problem is infeasible or unbounded; this occasionally happens during MIP presolve.

    source

    INFEASIBLE_POINT

    INTERRUPTED

    INVALID_MODEL

    INVALID_OPTION

    ITERATION_LIMIT

    LOCALLY_INFEASIBLE

    JuMP.LOCALLY_INFEASIBLE — Constant
    LOCALLY_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.

    source

    LOCALLY_SOLVED

    JuMP.LOCALLY_SOLVED — Constant
    LOCALLY_SOLVED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.

    source

    MANUAL

    JuMP.MANUAL — Constant

    moi_backend field holds a CachingOptimizer in MANUAL mode.

    source

    MAX_SENSE

    MEMORY_LIMIT

    MIN_SENSE

    NEARLY_FEASIBLE_POINT

    NEARLY_INFEASIBILITY_CERTIFICATE

    NEARLY_REDUCTION_CERTIFICATE

    NODE_LIMIT

    JuMP.NODE_LIMIT — Constant
    NODE_LIMIT::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    NODE_LIMIT: A branch-and-bound algorithm stopped because it explored a maximum number of nodes in the branch-and-bound tree.

    source

    NORM_LIMIT

    NO_SOLUTION

    NUMERICAL_ERROR

    OBJECTIVE_LIMIT

    OPTIMAL

    OPTIMIZE_NOT_CALLED

    OTHER_ERROR

    JuMP.OTHER_ERROR — Constant
    OTHER_ERROR::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    OTHER_ERROR: The algorithm stopped because of an error not covered by one of the statuses defined above.

    source

    OTHER_LIMIT

    OTHER_RESULT_STATUS

    JuMP.OTHER_RESULT_STATUS — Constant
    OTHER_RESULT_STATUS::ResultStatusCode

    An instance of the ResultStatusCode enum.

    OTHER_RESULT_STATUS: the result vector contains a solution with an interpretation not covered by one of the statuses defined above

    source

    REDUCTION_CERTIFICATE

    JuMP.REDUCTION_CERTIFICATE — Constant
    REDUCTION_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.

    source

    SLOW_PROGRESS

    JuMP.SLOW_PROGRESS — Constant
    SLOW_PROGRESS::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    SLOW_PROGRESS: The algorithm stopped because it was unable to continue making progress towards the solution.

    source

    SOLUTION_LIMIT

    JuMP.SOLUTION_LIMIT — Constant
    SOLUTION_LIMIT::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.

    source

    TIME_LIMIT

    UNKNOWN_RESULT_STATUS

    op_and

    JuMP.op_and — Constant
    op_and(x, y)

    A function that falls back to x & y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
+[x[1] + 2 x[2] - 5, 3 x[1] + 4 x[2] - 6] ∈ Zeros()
    source

    ALMOST_DUAL_INFEASIBLE

    ALMOST_INFEASIBLE

    ALMOST_LOCALLY_SOLVED

    JuMP.ALMOST_LOCALLY_SOLVED — Constant
    ALMOST_LOCALLY_SOLVED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    ALMOST_LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, or could not find directions for improvement within relaxed tolerances.

    source

    ALMOST_OPTIMAL

    AUTOMATIC

    DIRECT

    JuMP.DIRECT — Constant

    moi_backend field holds an AbstractOptimizer. No extra copy of the model is stored. The moi_backend must support add_constraint etc.

    source

    DUAL_INFEASIBLE

    JuMP.DUAL_INFEASIBLE — Constant
    DUAL_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.

    source

    FEASIBILITY_SENSE

    FEASIBLE_POINT

    INFEASIBILITY_CERTIFICATE

    JuMP.INFEASIBILITY_CERTIFICATE — Constant
    INFEASIBILITY_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.

    source

    INFEASIBLE

    INFEASIBLE_OR_UNBOUNDED

    JuMP.INFEASIBLE_OR_UNBOUNDED — Constant
    INFEASIBLE_OR_UNBOUNDED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    INFEASIBLE_OR_UNBOUNDED: The algorithm stopped because it decided that the problem is infeasible or unbounded; this occasionally happens during MIP presolve.

    source

    INFEASIBLE_POINT

    INTERRUPTED

    INVALID_MODEL

    INVALID_OPTION

    ITERATION_LIMIT

    LOCALLY_INFEASIBLE

    JuMP.LOCALLY_INFEASIBLE — Constant
    LOCALLY_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.

    source

    LOCALLY_SOLVED

    JuMP.LOCALLY_SOLVED — Constant
    LOCALLY_SOLVED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.

    source

    MANUAL

    JuMP.MANUAL — Constant

    moi_backend field holds a CachingOptimizer in MANUAL mode.

    source

    MAX_SENSE

    MEMORY_LIMIT

    MIN_SENSE

    NEARLY_FEASIBLE_POINT

    NEARLY_INFEASIBILITY_CERTIFICATE

    NEARLY_REDUCTION_CERTIFICATE

    NODE_LIMIT

    JuMP.NODE_LIMIT — Constant
    NODE_LIMIT::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    NODE_LIMIT: A branch-and-bound algorithm stopped because it explored a maximum number of nodes in the branch-and-bound tree.

    source

    NORM_LIMIT

    NO_SOLUTION

    NUMERICAL_ERROR

    OBJECTIVE_LIMIT

    OPTIMAL

    OPTIMIZE_NOT_CALLED

    OTHER_ERROR

    JuMP.OTHER_ERROR — Constant
    OTHER_ERROR::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    OTHER_ERROR: The algorithm stopped because of an error not covered by one of the statuses defined above.

    source

    OTHER_LIMIT

    OTHER_RESULT_STATUS

    JuMP.OTHER_RESULT_STATUS — Constant
    OTHER_RESULT_STATUS::ResultStatusCode

    An instance of the ResultStatusCode enum.

    OTHER_RESULT_STATUS: the result vector contains a solution with an interpretation not covered by one of the statuses defined above

    source

    REDUCTION_CERTIFICATE

    JuMP.REDUCTION_CERTIFICATE — Constant
    REDUCTION_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.

    source

    SLOW_PROGRESS

    JuMP.SLOW_PROGRESS — Constant
    SLOW_PROGRESS::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    SLOW_PROGRESS: The algorithm stopped because it was unable to continue making progress towards the solution.

    source

    SOLUTION_LIMIT

    JuMP.SOLUTION_LIMIT — Constant
    SOLUTION_LIMIT::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.

    source

    TIME_LIMIT

    UNKNOWN_RESULT_STATUS

    op_and

    JuMP.op_and — Constant
    op_and(x, y)

    A function that falls back to x & y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3155,7 +3155,7 @@
 false
 
 julia> op_and(true, x)
-true && x
    source

    op_equal_to

    JuMP.op_equal_to — Constant
    op_equal_to(x, y)

    A function that falls back to x == y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
+true && x
    source

    op_equal_to

    JuMP.op_equal_to — Constant
    op_equal_to(x, y)

    A function that falls back to x == y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3163,7 +3163,7 @@
 true
 
 julia> op_equal_to(x, 2)
-x == 2
    source

    op_greater_than_or_equal_to

    op_greater_than_or_equal_to

    JuMP.op_greater_than_or_equal_to — Constant
    op_greater_than_or_equal_to(x, y)

    A function that falls back to x >= y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3171,7 +3171,7 @@
 true
 
 julia> op_greater_than_or_equal_to(x, 2)
-x >= 2
    source

    op_less_than_or_equal_to

    op_less_than_or_equal_to

    JuMP.op_less_than_or_equal_to — Constant
    op_less_than_or_equal_to(x, y)

    A function that falls back to x <= y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3179,7 +3179,7 @@
 true
 
 julia> op_less_than_or_equal_to(x, 2)
-x <= 2
    source

    op_or

    JuMP.op_or — Constant
    op_or(x, y)

    A function that falls back to x | y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
+x <= 2
    source

    op_or

    JuMP.op_or — Constant
    op_or(x, y)

    A function that falls back to x | y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3187,7 +3187,7 @@
 true
 
 julia> op_or(true, x)
-true || x
    source

    op_strictly_greater_than

    op_strictly_greater_than

    JuMP.op_strictly_greater_than — Constant
    op_strictly_greater_than(x, y)

    A function that falls back to x > y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3195,7 +3195,7 @@
 false
 
 julia> op_strictly_greater_than(x, 2)
-x > 2
    source

    op_strictly_less_than

    op_strictly_less_than

    JuMP.op_strictly_less_than — Constant
    op_strictly_less_than(x, y)

    A function that falls back to x < y, but when called with JuMP variables or expressions, returns a GenericNonlinearExpr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3203,7 +3203,7 @@
 true
 
 julia> op_strictly_less_than(x, 2)
-x < 2
    source

    Base.empty!(::GenericModel)

    Base.empty! — Method
    empty!(model::GenericModel)::GenericModel

    Empty the model, that is, remove all variables, constraints and model attributes but not optimizer attributes. Always return the argument.

    Note: removes extensions data.

    Example

    julia> model = Model();
+x < 2
    source

    Base.empty!(::GenericModel)

    Base.empty! — Method
    empty!(model::GenericModel)::GenericModel

    Empty the model, that is, remove all variables, constraints and model attributes but not optimizer attributes. Always return the argument.

    Note: removes extensions data.

    Example

    julia> model = Model();
 
 julia> @variable(model, x[1:2]);
 
@@ -3223,7 +3223,7 @@
 Subject to
 
 julia> isempty(model)
-true
    source

    Base.isempty(::GenericModel)

    Base.isempty — Method
    isempty(model::GenericModel)

    Verifies whether the model is empty, that is, whether the MOI backend is empty and whether the model is in the same state as at its creation, apart from optimizer attributes.

    Example

    julia> model = Model();
+true
    source

    Base.isempty(::GenericModel)

    Base.isempty — Method
    isempty(model::GenericModel)

    Verifies whether the model is empty, that is, whether the MOI backend is empty and whether the model is in the same state as at its creation, apart from optimizer attributes.

    Example

    julia> model = Model();
 
 julia> isempty(model)
 true
@@ -3231,7 +3231,7 @@
 julia> @variable(model, x[1:2]);
 
 julia> isempty(model)
-false
    source

    Base.copy(::AbstractModel)

    Base.copy — Method
    copy(model::AbstractModel)

    Return a copy of the model model. It is similar to copy_model except that it does not return the mapping between the references of model and its copy.

    Note

    Model copy is not supported in DIRECT mode, that is, when a model is constructed using the direct_model constructor instead of the Model constructor. Moreover, independently on whether an optimizer was provided at model construction, the new model will have no optimizer, that is, an optimizer will have to be provided to the new model in the optimize! call.

    Example

    In the following example, a model model is constructed with a variable x and a constraint cref. It is then copied into a model new_model with the new references assigned to x_new and cref_new.

    julia> model = Model();
+false
    source

    Base.copy(::AbstractModel)

    Base.copy — Method
    copy(model::AbstractModel)

    Return a copy of the model model. It is similar to copy_model except that it does not return the mapping between the references of model and its copy.

    Note

    Model copy is not supported in DIRECT mode, that is, when a model is constructed using the direct_model constructor instead of the Model constructor. Moreover, independently on whether an optimizer was provided at model construction, the new model will have no optimizer, that is, an optimizer will have to be provided to the new model in the optimize! call.

    Example

    In the following example, a model model is constructed with a variable x and a constraint cref. It is then copied into a model new_model with the new references assigned to x_new and cref_new.

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -3245,12 +3245,12 @@
 x
 
 julia> cref_new = model[:cref]
-cref : x = 2
    source

    Base.write(::IO, ::GenericModel; ::MOI.FileFormats.FileFormat)

    Base.write(::IO, ::GenericModel; ::MOI.FileFormats.FileFormat)

    Base.write — Method
    Base.write(
     io::IO,
     model::GenericModel;
     format::MOI.FileFormats.FileFormat = MOI.FileFormats.FORMAT_MOF,
     kwargs...,
-)

    Write the JuMP model model to io in the format format.

    Other kwargs are passed to the Model constructor of the chosen format.

    source

    MOI.Utilities.reset_optimizer(::GenericModel)

    MOI.Utilities.drop_optimizer(::GenericModel)

    MOI.Utilities.attach_optimizer(::GenericModel)

    @NLconstraint

    JuMP.@NLconstraint — Macro
    @NLconstraint(model::GenericModel, expr)

    Add a constraint described by the nonlinear expression expr. See also @constraint.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLconstraint with @constraint.

    Example

    julia> model = Model();
+)

    Write the JuMP model model to io in the format format.

    Other kwargs are passed to the Model constructor of the chosen format.

    source

    MOI.Utilities.reset_optimizer(::GenericModel)

    MOI.Utilities.drop_optimizer(::GenericModel)

    MOI.Utilities.attach_optimizer(::GenericModel)

    @NLconstraint

    JuMP.@NLconstraint — Macro
    @NLconstraint(model::GenericModel, expr)

    Add a constraint described by the nonlinear expression expr. See also @constraint.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLconstraint with @constraint.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -3262,7 +3262,7 @@
 3-element Vector{NonlinearConstraintRef{ScalarShape}}:
  (sin(1.0 * x) - 1.0 / 1.0) - 0.0 ≤ 0
  (sin(2.0 * x) - 1.0 / 2.0) - 0.0 ≤ 0
- (sin(3.0 * x) - 1.0 / 3.0) - 0.0 ≤ 0
    source

    @NLconstraints

    JuMP.@NLconstraints — Macro
    @NLconstraints(model, args...)

    Adds multiple nonlinear constraints to model at once, in the same fashion as the @NLconstraint macro.

    The model must be the first argument, and multiple constraints can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the constraints that were defined.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLconstraints with @constraints.

    Example

    julia> model = Model();
+ (sin(3.0 * x) - 1.0 / 3.0) - 0.0 ≤ 0
    source

    @NLconstraints

    JuMP.@NLconstraints — Macro
    @NLconstraints(model, args...)

    Adds multiple nonlinear constraints to model at once, in the same fashion as the @NLconstraint macro.

    The model must be the first argument, and multiple constraints can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the constraints that were defined.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLconstraints with @constraints.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3278,7 +3278,7 @@
            t >= sqrt(x^2 + y^2)
            [i = 1:2], z[i] <= log(a[i])
        end)
-((t - sqrt(x ^ 2.0 + y ^ 2.0)) - 0.0 ≥ 0, NonlinearConstraintRef{ScalarShape}[(z[1] - log(4.0)) - 0.0 ≤ 0, (z[2] - log(5.0)) - 0.0 ≤ 0])
    source

    @NLexpression

    JuMP.@NLexpression — Macro
    @NLexpression(args...)

    Efficiently build a nonlinear expression which can then be inserted in other nonlinear constraints and the objective. See also [@expression].

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLexpression with @expression.

    Example

    julia> model = Model();
+((t - sqrt(x ^ 2.0 + y ^ 2.0)) - 0.0 ≥ 0, NonlinearConstraintRef{ScalarShape}[(z[1] - log(4.0)) - 0.0 ≤ 0, (z[2] - log(5.0)) - 0.0 ≤ 0])
    source

    @NLexpression

    JuMP.@NLexpression — Macro
    @NLexpression(args...)

    Efficiently build a nonlinear expression which can then be inserted in other nonlinear constraints and the objective. See also [@expression].

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLexpression with @expression.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -3299,7 +3299,7 @@
  subexpression[4]: sin(3.0 * x)
 
 julia> my_expr_2 = @NLexpression(model, log(1 + sum(exp(my_expr_1[i]) for i in 1:2)))
-subexpression[5]: log(1.0 + (exp(subexpression[2]) + exp(subexpression[3])))
    source

    @NLexpressions

    JuMP.@NLexpressions — Macro
    @NLexpressions(model, args...)

    Adds multiple nonlinear expressions to model at once, in the same fashion as the @NLexpression macro.

    The model must be the first argument, and multiple expressions can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the expressions that were defined.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLexpressions with @expressions.

    Example

    julia> model = Model();
+subexpression[5]: log(1.0 + (exp(subexpression[2]) + exp(subexpression[3])))
    source

    @NLexpressions

    JuMP.@NLexpressions — Macro
    @NLexpressions(model, args...)

    Adds multiple nonlinear expressions to model at once, in the same fashion as the @NLexpression macro.

    The model must be the first argument, and multiple expressions can be added on multiple lines wrapped in a begin ... end block.

    The macro returns a tuple containing the expressions that were defined.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLexpressions with @expressions.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
@@ -3313,7 +3313,7 @@
            my_expr, sqrt(x^2 + y^2)
            my_expr_1[i = 1:2], log(a[i]) - z[i]
        end)
-(subexpression[1]: sqrt(x ^ 2.0 + y ^ 2.0), NonlinearExpression[subexpression[2]: log(4.0) - z[1], subexpression[3]: log(5.0) - z[2]])
    source

    @NLobjective

    JuMP.@NLobjective — Macro
    @NLobjective(model, sense, expression)

    Add a nonlinear objective to model with optimization sense sense. sense must be Max or Min.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLobjective with @objective.

    Example

    julia> model = Model();
+(subexpression[1]: sqrt(x ^ 2.0 + y ^ 2.0), NonlinearExpression[subexpression[2]: log(4.0) - z[1], subexpression[3]: log(5.0) - z[2]])
    source

    @NLobjective

    JuMP.@NLobjective — Macro
    @NLobjective(model, sense, expression)

    Add a nonlinear objective to model with optimization sense sense. sense must be Max or Min.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace @NLobjective with @objective.

    Example

    julia> model = Model();
 
 julia> @variable(model, x)
 x
@@ -3322,7 +3322,7 @@
 
 julia> print(model)
 Max 2.0 * x + 1.0 + sin(x)
-Subject to
    source

    @NLparameter

    JuMP.@NLparameter — Macro
    @NLparameter(model, param == value)

    Create and return a nonlinear parameter param attached to the model model with initial value set to value. Nonlinear parameters may be used only in nonlinear expressions.

    Example

    julia> model = Model();
+Subject to
    source

    @NLparameter

    JuMP.@NLparameter — Macro
    @NLparameter(model, param == value)

    Create and return a nonlinear parameter param attached to the model model with initial value set to value. Nonlinear parameters may be used only in nonlinear expressions.

    Example

    julia> model = Model();
 
 julia> @NLparameter(model, x == 10)
 x == 10.0
@@ -3352,7 +3352,7 @@
  parameter[3] == 6.0
 
 julia> value(y[2])
-4.0
    source

    @NLparameters

    JuMP.@NLparameters — Macro
     @NLparameters(model, args...)

    Create and return multiple nonlinear parameters attached to model model, in the same fashion as @NLparameter macro.

    The model must be the first argument, and multiple parameters can be added on multiple lines wrapped in a begin ... end block. Distinct parameters need to be placed on separate lines as in the following example.

    The macro returns a tuple containing the parameters that were defined.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace a call like

    @NLparameters(model, begin
+4.0
    source

    @NLparameters

    JuMP.@NLparameters — Macro
     @NLparameters(model, args...)

    Create and return multiple nonlinear parameters attached to model model, in the same fashion as @NLparameter macro.

    The model must be the first argument, and multiple parameters can be added on multiple lines wrapped in a begin ... end block. Distinct parameters need to be placed on separate lines as in the following example.

    The macro returns a tuple containing the parameters that were defined.

    Compat

    This macro is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling. In most cases, you can replace a call like

    @NLparameters(model, begin
     p == value
 end)

    with

    @variables(model, begin
     p in Parameter(value)
@@ -3364,17 +3364,17 @@
        end);
 
 julia> value(x)
-10.0
    source

    add_nonlinear_constraint

    JuMP.add_nonlinear_constraint — Function
    add_nonlinear_constraint(model::Model, expr::Expr)

    Add a nonlinear constraint described by the Julia expression ex to model.

    This function is most useful if the expression ex is generated programmatically, and you cannot use @NLconstraint.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    Notes

    • You must interpolate the variables directly into the expression expr.

    Example

    julia> model = Model();
+10.0
    source

    add_nonlinear_constraint

    JuMP.add_nonlinear_constraint — Function
    add_nonlinear_constraint(model::Model, expr::Expr)

    Add a nonlinear constraint described by the Julia expression ex to model.

    This function is most useful if the expression ex is generated programmatically, and you cannot use @NLconstraint.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    Notes

    • You must interpolate the variables directly into the expression expr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> add_nonlinear_constraint(model, :($(x) + $(x)^2 <= 1))
-(x + x ^ 2.0) - 1.0 ≤ 0
    source

    add_nonlinear_expression

    JuMP.add_nonlinear_expression — Function
    add_nonlinear_expression(model::Model, expr::Expr)

    Add a nonlinear expression expr to model.

    This function is most useful if the expression expr is generated programmatically, and you cannot use @NLexpression.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    Notes

    • You must interpolate the variables directly into the expression expr.

    Example

    julia> model = Model();
+(x + x ^ 2.0) - 1.0 ≤ 0
    source

    add_nonlinear_expression

    JuMP.add_nonlinear_expression — Function
    add_nonlinear_expression(model::Model, expr::Expr)

    Add a nonlinear expression expr to model.

    This function is most useful if the expression expr is generated programmatically, and you cannot use @NLexpression.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    Notes

    • You must interpolate the variables directly into the expression expr.

    Example

    julia> model = Model();
 
 julia> @variable(model, x);
 
 julia> add_nonlinear_expression(model, :($(x) + $(x)^2))
-subexpression[1]: x + x ^ 2.0
    source

    add_nonlinear_parameter

    JuMP.add_nonlinear_parameter — Function
    add_nonlinear_parameter(model::Model, value::Real)

    Add an anonymous parameter to the model.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    all_nonlinear_constraints

    get_optimizer_attribute

    add_nonlinear_parameter

    JuMP.add_nonlinear_parameter — Function
    add_nonlinear_parameter(model::Model, value::Real)

    Add an anonymous parameter to the model.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    all_nonlinear_constraints

    get_optimizer_attribute

    JuMP.get_optimizer_attribute — Function
    get_optimizer_attribute(
     model::Union{GenericModel,MOI.OptimizerWithAttributes},
     attr::Union{AbstractString,MOI.AbstractOptimizerAttribute},
 )

    Return the value associated with the solver-specific attribute attr.

    If attr is an AbstractString, this is equivalent to get_optimizer_attribute(model, MOI.RawOptimizerAttribute(name)).

    Compat

    This method will remain in all v1.X releases of JuMP, but it may be removed in a future v2.0 release. We recommend using get_attribute instead.

    See also: set_optimizer_attribute, set_optimizer_attributes.

    Example

    julia> import Ipopt
@@ -3382,18 +3382,18 @@
 julia> model = Model(Ipopt.Optimizer);
 
 julia> get_optimizer_attribute(model, MOI.Silent())
-false
    source

    nonlinear_constraint_string

    nonlinear_constraint_string

    JuMP.nonlinear_constraint_string — Function
    nonlinear_constraint_string(
     model::GenericModel,
     mode::MIME,
     c::_NonlinearConstraint,
-)

    Return a string representation of the nonlinear constraint c belonging to model, given the mode.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    nonlinear_dual_start_value

    nonlinear_expr_string

    JuMP.nonlinear_expr_string — Function
    nonlinear_expr_string(
+)

    Return a string representation of the nonlinear constraint c belonging to model, given the mode.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    nonlinear_dual_start_value

    nonlinear_expr_string

    JuMP.nonlinear_expr_string — Function
    nonlinear_expr_string(
     model::GenericModel,
     mode::MIME,
     c::MOI.Nonlinear.Expression,
-)

    Return a string representation of the nonlinear expression c belonging to model, given the mode.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    nonlinear_model

    JuMP.nonlinear_model — Function
    nonlinear_model(
+)

    Return a string representation of the nonlinear expression c belonging to model, given the mode.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    nonlinear_model

    JuMP.nonlinear_model — Function
    nonlinear_model(
     model::GenericModel;
     force::Bool = false,
-)::Union{MOI.Nonlinear.Model,Nothing}

    If model has nonlinear components, return a MOI.Nonlinear.Model, otherwise return nothing.

    If force, always return a MOI.Nonlinear.Model, and if one does not exist for the model, create an empty one.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    num_nonlinear_constraints

    register

    JuMP.register — Function
    register(
+)::Union{MOI.Nonlinear.Model,Nothing}

    If model has nonlinear components, return a MOI.Nonlinear.Model, otherwise return nothing.

    If force, always return a MOI.Nonlinear.Model, and if one does not exist for the model, create an empty one.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source

    num_nonlinear_constraints

    register

    JuMP.register — Function
    register(
     model::Model,
     op::Symbol,
     dimension::Integer,
@@ -3421,7 +3421,7 @@
 
 julia> register(model, :g, 2, g; autodiff = true)
 
-julia> @NLobjective(model, Min, g(x[1], x[2]))
    source
    register(
+julia> @NLobjective(model, Min, g(x[1], x[2]))
    source
    register(
     model::Model,
     s::Symbol,
     dimension::Integer,
@@ -3460,7 +3460,7 @@
 
 julia> register(model, :g, 2, g, ∇g)
 
-julia> @NLobjective(model, Min, g(x[1], x[2]))
    source
    register(
+julia> @NLobjective(model, Min, g(x[1], x[2]))
    source
    register(
     model::Model,
     s::Symbol,
     dimension::Integer,
@@ -3484,7 +3484,7 @@
 julia> register(model, :foo, 1, f, ∇f, ∇²f)
 
 julia> @NLobjective(model, Min, foo(x))
-
    source

    set_nonlinear_dual_start_value

    set_nonlinear_dual_start_value

    JuMP.set_nonlinear_dual_start_value — Function
    set_nonlinear_dual_start_value(
     model::Model,
     start::Union{Nothing,Vector{Float64}},
 )

    Set the value of the MOI attribute MOI.NLPBlockDualStart.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    The start vector corresponds to the Lagrangian duals of the nonlinear constraints, in the order given by all_nonlinear_constraints. That is, you must pass a single start vector corresponding to all of the nonlinear constraints in a single function call; you cannot set the dual start value of nonlinear constraints one-by-one. The example below demonstrates how to use all_nonlinear_constraints to create a mapping between the nonlinear constraint references and the start vector.

    Pass nothing to unset a previous start.

    Example

    julia> model = Model();
@@ -3507,7 +3507,7 @@
 julia> nonlinear_dual_start_value(model)
 2-element Vector{Float64}:
  -1.0
-  1.0
    source

    set_nonlinear_objective

    set_nonlinear_objective

    JuMP.set_nonlinear_objective — Function
    set_nonlinear_objective(
     model::Model,
     sense::MOI.OptimizationSense,
     expr::Expr,
@@ -3515,17 +3515,17 @@
 
 julia> @variable(model, x);
 
-julia> set_nonlinear_objective(model, MIN_SENSE, :($(x) + $(x)^2))
    source

    set_normalized_coefficients

    set_normalized_coefficients

    JuMP.set_normalized_coefficients — Function
    set_normalized_coefficients(
     constraint::ConstraintRef{<:AbstractModel,<:MOI.ConstraintIndex{F}},
     variable::AbstractVariableRef,
     new_coefficients::Vector{Tuple{Int64,T}},
-) where {T,F<:Union{MOI.VectorAffineFunction{T},MOI.VectorQuadraticFunction{T}}}

    A deprecated method that now redirects to set_normalized_coefficient.

    source

    set_optimizer_attribute

    set_optimizer_attribute

    JuMP.set_optimizer_attribute — Function
    set_optimizer_attribute(
     model::Union{GenericModel,MOI.OptimizerWithAttributes},
     attr::Union{AbstractString,MOI.AbstractOptimizerAttribute},
     value,
 )

    Set the solver-specific attribute attr in model to value.

    If attr is an AbstractString, this is equivalent to set_optimizer_attribute(model, MOI.RawOptimizerAttribute(name), value).

    Compat

    This method will remain in all v1.X releases of JuMP, but it may be removed in a future v2.0 release. We recommend using set_attribute instead.

    See also: set_optimizer_attributes, get_optimizer_attribute.

    Example

    julia> model = Model();
 
-julia> set_optimizer_attribute(model, MOI.Silent(), true)
    source

    set_optimizer_attributes

    set_optimizer_attributes

    JuMP.set_optimizer_attributes — Function
    set_optimizer_attributes(
     model::Union{GenericModel,MOI.OptimizerWithAttributes},
     pairs::Pair...,
 )

    Given a list of attribute => value pairs, calls set_optimizer_attribute(model, attribute, value) for each pair.

    Compat

    This method will remain in all v1.X releases of JuMP, but it may be removed in a future v2.0 release. We recommend using set_attributes instead.

    See also: set_optimizer_attribute, get_optimizer_attribute.

    Example

    julia> import Ipopt
@@ -3538,7 +3538,7 @@
 
 julia> set_optimizer_attribute(model, "tol", 1e-4)
 
-julia> set_optimizer_attribute(model, "max_iter", 100)
    source

    set_value

    JuMP.set_value — Function
    set_value(p::NonlinearParameter, v::Number)

    Store the value v in the nonlinear parameter p.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    Example

    julia> model = Model();
+julia> set_optimizer_attribute(model, "max_iter", 100)
    source

    set_value

    JuMP.set_value — Function
    set_value(p::NonlinearParameter, v::Number)

    Store the value v in the nonlinear parameter p.

    Compat

    This function is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    Example

    julia> model = Model();
 
 julia> @NLparameter(model, p == 0)
 p == 0.0
@@ -3547,4 +3547,4 @@
 5
 
 julia> value(p)
-5.0
    source

    NonlinearConstraintIndex

    NonlinearConstraintRef

    NonlinearExpression

    NonlinearParameter

    JuMP.NonlinearParameter — Type
    NonlinearParameter <: AbstractJuMPScalar

    A struct to represent a nonlinear parameter.

    Create a parameter using @NLparameter.

    Compat

    This type is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source
    +5.0source

    NonlinearConstraintIndex

    NonlinearConstraintRef

    NonlinearExpression

    NonlinearParameter

    JuMP.NonlinearParameter — Type
    NonlinearParameter <: AbstractJuMPScalar

    A struct to represent a nonlinear parameter.

    Create a parameter using @NLparameter.

    Compat

    This type is part of the legacy nonlinear interface. Consider using the new nonlinear interface documented in Nonlinear Modeling.

    source
    diff --git a/previews/PR3913/background/algebraic_modeling_languages/index.html b/previews/PR3913/background/algebraic_modeling_languages/index.html index 38075eb48f0..d9d94b2e34c 100644 --- a/previews/PR3913/background/algebraic_modeling_languages/index.html +++ b/previews/PR3913/background/algebraic_modeling_languages/index.html @@ -138,4 +138,4 @@ julia> highs_knapsack([1.0, 2.0], [0.5, 0.5], 1.25) 2-element Vector{Float64}: 0.0 - 2.0

    We've now gone from a algebraic model that looked identical to the mathematical model we started with, to a verbose function that uses HiGHS-specific functionality.

    The difference between algebraic_knapsack and highs_knapsack highlights the benefit that algebraic modeling languages provide to users. Moreover, if we used a different solver, the solver-specific function would be entirely different. A key benefit of an algebraic modeling language is that you can change the solver without needing to rewrite the model.

    + 2.0

    We've now gone from a algebraic model that looked identical to the mathematical model we started with, to a verbose function that uses HiGHS-specific functionality.

    The difference between algebraic_knapsack and highs_knapsack highlights the benefit that algebraic modeling languages provide to users. Moreover, if we used a different solver, the solver-specific function would be entirely different. A key benefit of an algebraic modeling language is that you can change the solver without needing to rewrite the model.

    diff --git a/previews/PR3913/background/bibliography/index.html b/previews/PR3913/background/bibliography/index.html index 49048181aaf..5699efeee17 100644 --- a/previews/PR3913/background/bibliography/index.html +++ b/previews/PR3913/background/bibliography/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Bibliography

    +
    GitHub

    Bibliography

    diff --git a/previews/PR3913/changelog/index.html b/previews/PR3913/changelog/index.html index 2e581b43cb5..b61e67a6033 100644 --- a/previews/PR3913/changelog/index.html +++ b/previews/PR3913/changelog/index.html @@ -12,4 +12,4 @@ new_b = backend(model)

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  • All usages of @SDconstraint are deprecated. The new syntax is @constraint(model, X >= Y, PSDCone()).
  • Creating a DenseAxisArray with a Number as an axis will now display a warning. This catches a common error in which users write @variable(model, x[length(S)]) instead of @variable(model, x[1:length(S)]).
  • The caching_mode argument to Model, for example, Model(caching_mode = MOIU.MANUAL) mode has been removed. For more control over the optimizer, use direct_model instead.
  • The previously deprecated lp_objective_perturbation_range and lp_rhs_perturbation_range functions have been removed. Use lp_sensitivity_report instead.
  • The .m fields of NonlinearExpression and NonlinearParameter have been renamed to .model.
  • Infinite variable bounds are now ignored. Thus, @variable(model, x <= Inf) will show has_upper_bound(x) == false. Previously, these bounds were passed through to the solvers which caused numerical issues for solvers expecting finite bounds.
  • The variable_type and constraint_type functions were removed. This should only affect users who previously wrote JuMP extensions. The functions can be deleted without consequence.
  • The internal functions moi_mode, moi_bridge_constraints, moi_add_constraint, and moi_add_to_function_constant are no longer exported.
  • The un-used method Containers.generate_container has been deleted.
  • The Containers API has been refactored, and _build_ref_sets is now public as Containers.build_ref_sets.
  • The parse_constraint_ methods for extending @constraint at parse time have been refactored in a breaking way. Consult the Extensions documentation for more details and examples.

    • Added

    • The TerminationStatusCode and ResultStatusCode enums are now exported by JuMP. Prefer termination_status(model) == OPTIMAL instead of == MOI.OPTIMAL, although the MOI. prefix way still works.
    • Copy a x::DenseAxisArray to an Array by calling Array(x).
    • NonlinearExpression is now a subtype of AbstractJuMPScalar
    • Constraints such as @constraint(model, x + 1 in MOI.Integer()) are now supported.
    • primal_feasibility_report now accepts a function as the first argument.
    • Scalar variables @variable(model, x[1:2] in MOI.Integer()) creates two variables, both of which are constrained to be in the set MOI.Integer.
    • Conic constraints can now be specified as inequalities under a different partial ordering. So @constraint(model, x - y in MOI.Nonnegatives()) can now be written as @constraint(model, x >= y, MOI.Nonnegatives()).
    • Names are now set for vectorized constraints.

    Fixed

    • Fixed a performance issue when show was called on a SparseAxisArray with a large number of elements.
    • Fixed a bug displaying barrier and simplex iterations in solution_summary.
    • Fixed a bug by implementing hash for DenseAxisArray and SparseAxisArray.
    • Names are now only set if the solver supports them. Previously, this prevented solvers such as Ipopt from being used with direct_model.
    • MutableArithmetics.Zero is converted into a 0.0 before being returned to the user. Previously, some calls to @expression would return the undocumented MutableArithmetics.Zero() object. One example is summing over an empty set @expression(model, sum(x[i] for i in 1:0)). You will now get 0.0 instead.
    • AffExpr and QuadExpr can now be used with == 0 instead of iszero. This fixes a number of issues relating to Julia standard libraries such as LinearAlgebra and SparseArrays.
    • Fixed a bug when registering a user-defined function with splatting.

    Other

    • The documentation is now available as a PDF.
    • The documentation now includes a full copy of the MathOptInterface documentation to make it easy to link concepts between the docs. (The MathOptInterface documentation has also been significantly improved.)
    • The documentation contains a large number of improvements and clarifications on a range of topics. Thanks to @sshin23, @DilumAluthge, and @jlwether.
    • The documentation is now built with Julia 1.6 instead of 1.0.
    • Various error messages have been improved to be more readable.

    Version 0.21.10 (September 4, 2021)

    Added

    • Added add_NL_expression
    • add_NL_xxx functions now support AffExpr and QuadExpr as terms

    Fixed

    • Fixed a bug in solution_summary
    • Fixed a bug in relax_integrality

    Other

    • Improved error message in lp_sensitivity_report

    Version 0.21.9 (August 1, 2021)

    Added

    • Containers now support arbitrary container types by passing the type to the container keyword and overloading Containers.container.
    • is_valid now supports nonlinear constraints
    • Added unsafe_backend for querying the inner-most optimizer of a JuMP model.
    • Nonlinear parameters now support the plural @NLparameters macro.
    • Containers (for example, DenseAxisArray) can now be used in vector-valued constraints.

    Other

    • Various improvements to the documentation.

    Version 0.21.8 (May 8, 2021)

    Added

    • The @constraint macro is now extendable in the same way as @variable.
    • AffExpr and QuadExpr can now be used in nonlinear macros.

    Fixed

    • Fixed a bug in lp_sensitivity_report.
    • Fixed an inference issue when creating empty SparseAxisArrays.

    Version 0.21.7 (April 12, 2021)

    Added

    • Added primal_feasibility_report, which can be used to check whether a primal point satisfies primal feasibility.
    • Added coefficient, which returns the coefficient associated with a variable in affine and quadratic expressions.
    • Added copy_conflict, which returns the IIS of an infeasible model.
    • Added solution_summary, which returns (and prints) a struct containing a summary of the solution.
    • Allow AbstractVector in vector constraints instead of just Vector.
    • Added latex_formulation(model) which returns an object representing the latex formulation of a model. Use print(latex_formulation(model)) to print the formulation as a string.
    • User-defined functions in nonlinear expressions are now automatically registered to aid quick model prototyping. However, a warning is printed to encourage the manual registration.
    • DenseAxisArray's now support broadcasting over multiple arrays.
    • Container indices can now be iterators of Base.SizeUnknown.

    Fixed

    • Fixed bug in rad2deg and deg2rad in nonlinear expressions.
    • Fixed a MethodError bug in Containers when forcing container type.
    • Allow partial slicing of a DenseAxisArray, resolving an issue from 2014.
    • Fixed a bug printing variable names in IJulia.
    • Ending an IJulia cell with model now prints a summary of the model (like in the REPL) not the latex formulation. Use print(model) to print the latex formulation.
    • Fixed a bug when copying models containing nested arrays.

    Other

    • Tutorials are now part of the documentation, and more refactoring has taken place.
    • Added JuliaFormatter added as a code formatter.
    • Added some precompilation statements to reduce initial latency.
    • Various improvements to error messages to make them more helpful.
    • Improved performance of value(::NonlinearExpression).
    • Improved performance of fix(::VariableRef).

    Version 0.21.6 (January 29, 2021)

    Added

    • Added support for skew symmetric variables via @variable(model, X[1:2, 1:2] in SkewSymmetricMatrixSpace()).
    • lp_sensitivity_report has been added which significantly improves the performance of querying the sensitivity summary of an LP. lp_objective_perturbation_range and lp_rhs_perturbation_range are deprecated.
    • Dual warm-starts are now supported with set_dual_start_value and dual_start_value.
    • ∈ (\in<tab>) can now be used in macros instead of = or in.
    • Use haskey(model::Model, key::Symbol) to check if a name key is registered in a model.
    • Added unregister(model::Model, key::Symbol) to unregister a name key from model.
    • Added callback_node_status for use in callbacks.
    • Added print_bridge_graph to visualize the bridging graph generated by MathOptInterface.
    • Improved error message for containers with duplicate indices.

    Fixed

    • Various fixes to pass tests on Julia 1.6.
    • Fixed a bug in the printing of nonlinear expressions in IJulia.
    • Fixed a bug when nonlinear expressions are passed to user-defined functions.
    • Some internal functions that were previously exported are now no longer exported.
    • Fixed a bug when relaxing a fixed binary variable.
    • Fixed a StackOverflowError that occurred when SparseAxisArrays had a large number of elements.
    • Removed an unnecessary type assertion in list_of_constraint_types.
    • Fixed a bug when copying models with registered expressions.

    Other

    • The documentation has been significantly overhauled. It now has distinct sections for the manual, API reference, and examples. The existing examples in /examples have now been moved to /docs/src/examples and rewritten using Literate.jl, and they are now included in the documentation.
    • JuliaFormatter has been applied to most of the codebase. This will continue to roll out over time, as we fix upstream issues in the formatter, and will eventually become compulsory.
    • The root cause of a large number of method invalidations has been resolved.
    • We switched continuous integration from Travis and Appveyor to GitHub Actions.

    Version 0.21.5 (September 18, 2020)

    Fixed

    • Fixed deprecation warnings
    • Throw DimensionMismatch for incompatibly sized functions and sets
    • Unify treatment of keys(x) on JuMP containers

    Version 0.21.4 (September 14, 2020)

    Added

    • Add debug info when adding unsupported constraints
    • Add relax_integrality for solving continuous relaxation
    • Allow querying constraint conflicts

    Fixed

    • Dispatch on Real for MOI.submit
    • Implement copy for CustomSet in tests
    • Don't export private macros
    • Fix invalid assertion in nonlinear
    • Error if constraint has NaN right-hand side
    • Improve speed of tests
    • Lots of work modularizing files in /test
    • Improve line numbers in macro error messages
    • Print nonlinear subexpressions
    • Various documentation updates
    • Dependency updates:
      • Datastructures 0.18
      • MathOptFormat v0.5
      • Prep for MathOptInterface 0.9.15

    Version 0.21.3 (June 18, 2020)

    • Added Special Order Sets (SOS1 and SOS2) to JuMP with default weights to ease the creation of such constraints (#2212).
    • Added functions simplex_iterations, barrier_iterations and node_count (#2201).
    • Added function reduced_cost (#2205).
    • Implemented callback_value for affine and quadratic expressions (#2231).
    • Support MutableArithmetics.Zero in objective and constraints (#2219).
    • Documentation improvements:
      • Mention tutorials in the docs (#2223).
      • Update COIN-OR links (#2242).
      • Explicit link to the documentation of MOI.FileFormats (#2253).
      • Typo fixes (#2261).
    • Containers improvements:
      • Fix Base.map for DenseAxisArray (#2235).
      • Throw BoundsError if number of indices is incorrect for DenseAxisArray and SparseAxisArray (#2240).
    • Extensibility improvements:
      • Implement a set_objective method fallback that redirects to set_objective_sense and set_objective_function (#2247).
      • Add parse_constraint method with arbitrary number of arguments (#2051).
      • Add parse_constraint_expr and parse_constraint_head (#2228).

    Version 0.21.2 (April 2, 2020)

    • Added relative_gap() to access MOI.RelativeGap() attribute (#2199).
    • Documentation fixes:
      • Added link to source for docstrings in the documentation (#2207).
      • Added docstring for @variables macro (#2216).
      • Typo fixes (#2177, #2184, #2182).
    • Implementation of methods for Base functions:
      • Implemented Base.empty! for JuMP.Model (#2198).
      • Implemented Base.conj for JuMP scalar types (#2209).

    Fixed

    • Fixed sum of expression with scalar product in macro (#2178).
    • Fixed writing of nonlinear models to MathOptFormat (#2181).
    • Fixed construction of empty SparseAxisArray (#2179).
    • Fixed constraint with zero function (#2188).

    Version 0.21.1 (Feb 18, 2020)

    • Improved the clarity of the with_optimizer deprecation warning.

    Version 0.21.0 (Feb 16, 2020)

    Breaking

    • Deprecated with_optimizer (#2090, #2084, #2141). You can replace with_optimizer by either nothing, optimizer_with_attributes or a closure:

      • replace with_optimizer(Ipopt.Optimizer) by Ipopt.Optimizer.
      • replace with_optimizer(Ipopt.Optimizer, max_cpu_time=60.0) by optimizer_with_attributes(Ipopt.Optimizer, "max_cpu_time" => 60.0).
      • replace with_optimizer(Gurobi.Optimizer, env) by () -> Gurobi.Optimizer(env).
      • replace with_optimizer(Gurobi.Optimizer, env, Presolve=0) by optimizer_with_attributes(() -> Gurobi.Optimizer(env), "Presolve" => 0).

      alternatively to optimizer_with_attributes, you can also set the attributes separately with set_optimizer_attribute.

    • Renamed set_parameter and set_parameters to set_optimizer_attribute and set_optimizer_attributes (#2150).

    • Broadcast should now be explicit inside macros. @SDconstraint(model, x >= 1) and @constraint(model, x + 1 in SecondOrderCone()) now throw an error instead of broadcasting 1 along the dimension of x (#2107).

    • @SDconstraint(model, x >= 0) is now equivalent to @constraint(model, x in PSDCone()) instead of @constraint(model, (x .- 0) in PSDCone()) (#2107).

    • The macros now create the containers with map instead of for loops, as a consequence, containers created by @expression can now have any element type and containers of constraint references now have concrete element types when possible. This fixes a long-standing issue where @expression could only be used to generate a collection of linear expressions. Now it works for quadratic expressions as well (#2070).

    • Calling deepcopy(::AbstractModel) now throws an error.

    • The constraint name is now printed in the model string (#2108).

    Added

    • Added support for solver-independent and solver-specific callbacks (#2101).
    • Added write_to_file and read_from_file, supported formats are CBF, LP, MathOptFormat, MPS and SDPA (#2114).
    • Added support for complementarity constraints (#2132).
    • Added support for indicator constraints (#2092).
    • Added support for querying multiple solutions with the result keyword (#2100).
    • Added support for constraining variables on creation (#2128).
    • Added method delete that deletes a vector of variables at once if it is supported by the underlying solver (#2135).
    • The arithmetic between JuMP expression has be refactored into the MutableArithmetics package (#2107).
    • Improved error on complex values in NLP (#1978).
    • Added an example of column generation (#2010).

    Fixed

    • Incorrect coefficients generated when using Symmetric variables (#2102)

    Version 0.20.1 (Oct 18, 2019)

    • Add sections on @variables and @constraints in the documentation (#2062).
    • Fixed product of sparse matrices for Julia v1.3 (#2063).
    • Added set_objective_coefficient to modify the coefficient of a linear term of the objective function (#2008).
    • Added set_time_limit_sec, unset_time_limit_sec and time_limit_sec to set and query the time limit for the solver in seconds (#2053).

    Version 0.20.0 (Aug 24, 2019)

    • Documentation updates.
    • Numerous bug fixes.
    • Better error messages (#1977, #1978, #1997, #2017).
    • Performance improvements (#1947, #2032).
    • Added LP sensitivity summary functions lp_objective_perturbation_range and lp_rhs_perturbation_range (#1917).
    • Added functions dual_objective_value, raw_status and set_parameter.
    • Added function set_objective_coefficient to modify the coefficient of a linear term of the objective (#2008).
    • Added functions set_normalized_rhs, normalized_rhs, and add_to_function_constant to modify and get the constant part of a constraint (#1935, #1960).
    • Added functions set_normalized_coefficient and normalized_coefficient to modify and get the coefficient of a linear term of a constraint (#1935, #1960).
    • Numerous other improvements in MOI 0.9, see the NEWS.md file of MOI for more details.

    Version 0.19.2 (June 8, 2019)

    • Fix a bug in derivatives that could arise in models with nested nonlinear subexpressions.

    Version 0.19.1 (May 12, 2019)

    • Usability and performance improvements.
    • Bug fixes.

    Version 0.19.0 (February 15, 2019)

    JuMP 0.19 contains significant breaking changes.

    Breaking

    • JuMP's abstraction layer for communicating with solvers changed from MathProgBase (MPB) to MathOptInterface (MOI). MOI addresses many longstanding design issues. (See @mlubin's slides from JuMP-dev 2018.) JuMP 0.19 is compatible only with solvers that have been updated for MOI. See the installation guide for a list of solvers that have and have not yet been updated.

    • Most solvers have been renamed to PackageName.Optimizer. For example, GurobiSolver() is now Gurobi.Optimizer.

    • Solvers are no longer added to a model via Model(solver = XXX(kwargs...)). Instead use Model(with_optimizer(XXX, kwargs...)). For example, Model(with_optimizer(Gurobi.Optimizer, OutputFlag=0)).

    • JuMP containers (for example, the objects returned by @variable) have been redesigned. Containers.SparseAxisArray replaces JuMPDict, JuMPArray was rewritten (inspired by AxisArrays) and renamed Containers.DenseAxisArray, and you can now request a container type with the container= keyword to the macros. See the corresponding documentation for more details.

    • The statuses returned by solvers have changed. See the possible status values here. The MOI statuses are much richer than the MPB statuses and can be used to distinguish between previously indistinguishable cases (for example, did the solver have a feasible solution when it stopped because of the time limit?).

    • Starting values are separate from result values. Use value to query the value of a variable in a solution. Use start_value and set_start_value to get and set an initial starting point provided to the solver. The solutions from previous solves are no longer automatically set as the starting points for the next solve.

    • The data structures for affine and quadratic expressions AffExpr and QuadExpr have changed. Internally, terms are stored in dictionaries instead of lists. Duplicate coefficients can no longer exist. Accessors and iteration methods have changed.

    • JuMPNLPEvaluator no longer includes the linear and quadratic parts of the model in the evaluation calls. These are now handled separately to allow NLP solvers that support various types of constraints.

    • JuMP solver-independent callbacks have been replaced by solver-specific callbacks. See your favorite solver for more details. (See the note below: No solver-specific callbacks are implemented yet.)

    • The norm() syntax is no longer recognized inside macros. Use the SecondOrderCone() set instead.

    • JuMP no longer performs automatic transformation between special quadratic forms and second-order cone constraints. Support for these constraint classes depends on the solver.

    • The symbols :Min and :Max are no longer used as optimization senses. Instead, JuMP uses the OptimizationSense enum from MathOptInterface. @objective(model, Max, ...), @objective(model, Min, ...), @NLobjective(model, Max, ...), and @objective(model, Min, ...) remain valid, but @objective(m, :Max, ...) is no longer accepted.

    • The sign conventions for duals has changed in some cases for consistency with conic duality (see the documentation). The shadow_price helper method returns duals with signs that match conventional LP interpretations of dual values as sensitivities of the objective value to relaxations of constraints.

    • @constraintref is no longer defined. Instead, create the appropriate container to hold constraint references manually. For example,

      constraints = Dict() # Optionally, specify types for improved performance.
 for i in 1:N
   constraints[i] = @constraint(model, ...)
-end

    • The lowerbound, upperbound, and basename keyword arguments to the @variable macro have been renamed to lower_bound, upper_bound, and base_name, for consistency with JuMP's new style recommendations.

    • We rely on broadcasting syntax to apply accessors to collections of variables, for example, value.(x) instead of getvalue(x) for collections. (Use value(x) when x is a scalar object.)

    Added

    • Splatting (like f(x...)) is recognized in restricted settings in nonlinear expressions.

    • Support for deleting constraints and variables.

    • The documentation has been completely rewritten using docstrings and Documenter.

    • Support for modeling mixed conic and quadratic models (for example, conic models with quadratic objectives and bi-linear matrix inequalities).

    • Significantly improved support for modeling new types of constraints and for extending JuMP's macros.

    • Support for providing dual warm starts.

    • Improved support for accessing solver-specific attributes (for example, the irreducible inconsistent subsystem).

    • Explicit control of whether symmetry-enforcing constraints are added to PSD constraints.

    • Support for modeling exponential cones.

    • Significant improvements in internal code quality and testing.

    • Style and naming guidelines.

    • Direct mode and manual mode provide explicit control over when copies of a model are stored or regenerated. See the corresponding documentation.

    Regressions

    There are known regressions from JuMP 0.18 that will be addressed in a future release (0.19.x or later):

    • Performance regressions in model generation (issue). Please file an issue anyway if you notice a significant performance regression. We have plans to address a number of performance issues, but we might not be aware of all of them.

    • Fast incremental NLP solves are not yet reimplemented (issue).

    • We do not yet have an implementation of solver-specific callbacks.

    • The column generation syntax in @variable has been removed (that is, the objective, coefficients, and inconstraints keyword arguments). Support for column generation will be re-introduced in a future release.

    • The ability to solve the continuous relaxation (that is, via solve(model; relaxation = true)) is not yet reimplemented (issue).

    Version 0.18.5 (December 1, 2018)

    • Support views in some derivative evaluation functions.
    • Improved compatibility with PackageCompiler.

    Version 0.18.4 (October 8, 2018)

    • Fix a bug in model printing on Julia 0.7 and 1.0.

    Version 0.18.3 (October 1, 2018)

    • Add support for Julia v1.0 (Thanks @ExpandingMan)
    • Fix matrix expressions with quadratic functions (#1508)

    Version 0.18.2 (June 10, 2018)

    • Fix a bug in second-order derivatives when expressions are present (#1319)
    • Fix a bug in @constraintref (#1330)

    Version 0.18.1 (April 9, 2018)

    • Fix for nested tuple destructuring (#1193)
    • Preserve internal model when relaxation=true (#1209)
    • Minor bug fixes and updates for example

    Version 0.18.0 (July 27, 2017)

    • Drop support for Julia 0.5.
    • Update for ForwardDiff 0.5.
    • Minor bug fixes.

    Version 0.17.1 (June 9, 2017)

    • Use of constructconstraint! in @SDconstraint.
    • Minor bug fixes.

    Version 0.17.0 (May 27, 2017)

    • Breaking change: Mixing quadratic and conic constraints is no longer supported.
    • Breaking change: The getvariable and getconstraint functions are replaced by indexing on the corresponding symbol. For instance, to access the variable with name x, one should now write m[:x] instead of getvariable(m, :x). As a consequence, creating a variable and constraint with the same name now triggers a warning, and accessing one of them afterwards throws an error. This change is breaking only in the latter case.
    • Addition of the getobjectivebound function that mirrors the functionality of the MathProgBase getobjbound function except that it takes into account transformations performed by JuMP.
    • Minor bug fixes.

    The following changes are primarily of interest to developers of JuMP extensions:

    • The new syntax @constraint(model, expr in Cone) creates the constraint ensuring that expr is inside Cone. The Cone argument is passed to constructconstraint! which enables the call to the dispatched to an extension.
    • The @variable macro now calls constructvariable! instead of directly calling the Variable constructor. Extra arguments and keyword arguments passed to @variable are passed to constructvariable! which enables the call to be dispatched to an extension.
    • Refactor the internal function conicdata (used build the MathProgBase conic model) into smaller sub-functions to make these parts reusable by extensions.

    Version 0.16.2 (March 28, 2017)

    • Minor bug fixes and printing tweaks
    • Address deprecation warnings for Julia 0.6

    Version 0.16.1 (March 7, 2017)

    • Better support for AbstractArray in JuMP (Thanks @tkoolen)
    • Minor bug fixes

    Version 0.16.0 (February 23, 2017)

    • Breaking change: JuMP no longer has a mechanism for selecting solvers by default (the previous mechanism was flawed and incompatible with Julia 0.6). Not specifying a solver before calling solve() will result in an error.
    • Breaking change: User-defined functions are no longer global. The first argument to JuMP.register is now a JuMP Model object within whose scope the function will be registered. Calling JuMP.register without a Model now produces an error.
    • Breaking change: Use the new JuMP.fix method to fix a variable to a value or to update the value to which a variable is fixed. Calling setvalue on a fixed variable now results in an error in order to avoid silent behavior changes. (Thanks @joaquimg)
    • Nonlinear expressions now print out similarly to linear/quadratic expressions (useful for debugging!)
    • New category keyword to @variable. Used for specifying categories of anonymous variables.
    • Compatibility with Julia 0.6-dev.
    • Minor fixes and improvements (Thanks @cossio, @ccoffrin, @blegat)

    Version 0.15.1 (January 31, 2017)

    • Bugfix for @LinearConstraints and friends

    Version 0.15.0 (December 22, 2016)

    • Julia 0.5.0 is the minimum required version for this release.
    • Document support for BARON solver
    • Enable info callbacks in more states than before, for example, for recording solutions. New when argument to addinfocallback (#814, thanks @yeesian)
    • Improved support for anonymous variables. This includes new warnings for potentially confusing use of the traditional non-anonymous syntax:
      • When multiple variables in a model are given the same name
      • When non-symbols are used as names, for example, @variable(m, x[1][1:N])
    • Improvements in iterating over JuMP containers (#836, thanks @IssamT)
    • Support for writing variable names in .lp file output (Thanks @leethargo)
    • Support for querying duals to SDP problems (Thanks @blegat)
    • The comprehension syntax with curly braces sum{}, prod{}, and norm2{} has been deprecated in favor of Julia's native comprehension syntax sum(), prod() and norm() as previously announced. (For early adopters of the new syntax, norm2() was renamed to norm() without deprecation.)
    • Unit tests rewritten to use Base.Test instead of FactCheck
    • Improved support for operations with matrices of JuMP types (Thanks @ExpandingMan)
    • The syntax to halt a solver from inside a callback has changed from throw(CallbackAbort()) to return JuMP.StopTheSolver
    • Minor bug fixes

    Version 0.14.2 (December 12, 2016)

    • Allow singleton anonymous variables (includes bugfix)

    Version 0.14.1 (September 12, 2016)

    • More consistent handling of states in informational callbacks, includes a new when parameter to addinfocallback for specifying in which state an informational callback should be called.

    Version 0.14.0 (August 7, 2016)

    • Compatibility with Julia 0.5 and ForwardDiff 0.2
    • Support for "anonymous" variables, constraints, expressions, and parameters, for example, x = @variable(m, [1:N]) instead of @variable(m, x[1:N])
    • Support for retrieving constraints from a model by name via getconstraint
    • @NLconstraint now returns constraint references (as expected).
    • Support for vectorized expressions within lazy constraints
    • On Julia 0.5, parse new comprehension syntax sum(x[i] for i in 1:N if isodd(i)) instead of sum{ x[i], i in 1:N; isodd(i) }. The old syntax with curly braces will be deprecated in JuMP 0.15.
    • Now possible to provide nonlinear expressions as "raw" Julia Expr objects instead of using JuMP's nonlinear macros. This input format is useful for programmatically generated expressions.
    • s/Mathematical Programming/Mathematical Optimization/
    • Support for local cuts (Thanks to @madanim, Mehdi Madani)
    • Document Xpress interface developed by @joaquimg, Joaquim Dias Garcia
    • Minor bug and deprecation fixes (Thanks @odow, @jrevels)

    Version 0.13.2 (May 16, 2016)

    • Compatibility update for MathProgBase

    Version 0.13.1 (May 3, 2016)

    • Fix broken deprecation for registerNLfunction.

    Version 0.13.0 (April 29, 2016)

    • Most exported methods and macros have been renamed to avoid camelCase. See the list of changes here. There is a 1-1 mapping from the old names to the new, and it is safe to simply replace the names to update existing models.
    • Specify variable lower/upper bounds in @variable using the lowerbound and upperbound keyword arguments.
    • Change name printed for variable using the basename keyword argument to @variable.
    • New @variables macro allows multi-line declaration of groups of variables.
    • A number of solver methods previously available only through MathProgBase are now exposed directly in JuMP. The fix was recorded live.
    • Compatibility fixes with Julia 0.5.
    • The "end" indexing syntax is no longer supported within JuMPArrays which do not use 1-based indexing until upstream issues are resolved, see here.

    Version 0.12.2 (March 9, 2016)

    • Small fixes for nonlinear optimization

    Version 0.12.1 (March 1, 2016)

    • Fix a regression in slicing for JuMPArrays (when not using 1-based indexing)

    Version 0.12.0 (February 27, 2016)

    • The automatic differentiation functionality has been completely rewritten with a number of user-facing changes:
      • @defExpr and @defNLExpr now take the model as the first argument. The previous one-argument version of @defExpr is deprecated; all expressions should be named. For example, replace @defExpr(2x+y) with @defExpr(jump_model, my_expr, 2x+y).
      • JuMP no longer uses Julia's variable binding rules for efficiently re-solving a sequence of nonlinear models. Instead, we have introduced nonlinear parameters. This is a breaking change, so we have added a warning message when we detect models that may depend on the old behavior.
      • Support for user-defined functions integrated within nonlinear JuMP expressions.
    • Replaced iteration over AffExpr with Number-like scalar iteration; previous iteration behavior is now available via linearterms(::AffExpr).
    • Stopping the solver via throw(CallbackAbort()) from a callback no longer triggers an exception. Instead, solve() returns UserLimit status.
    • getDual() now works for conic problems (Thanks @emreyamangil.)

    Version 0.11.3 (February 4, 2016)

    • Bug-fix for problems with quadratic objectives and semidefinite constraints

    Version 0.11.2 (January 14, 2016)

    • Compatibility update for Mosek

    Version 0.11.1 (December 1, 2015)

    • Remove usage of @compat in tests.
    • Fix updating quadratic objectives for nonlinear models.

    Version 0.11.0 (November 30, 2015)

    • Julia 0.4.0 is the minimum required version for this release.
    • Fix for scoping semantics of index variables in sum{}. Index variables no longer leak into the surrounding scope.
    • Addition of the solve(m::Model, relaxation=true) keyword argument to solve the standard continuous relaxation of model m
    • The getConstraintBounds() method allows access to the lower and upper bounds of all constraints in a (nonlinear) model.
    • Update for breaking changes in MathProgBase

    Version 0.10.3 (November 20, 2015)

    • Fix a rare error when parsing quadratic expressions
    • Fix Variable() constructor with default arguments
    • Detect unrecognized keywords in solve()

    Version 0.10.2 (September 28, 2015)

    • Fix for deprecation warnings

    Version 0.10.1 (September 3, 2015)

    • Fixes for ambiguity warnings.
    • Fix for breaking change in precompilation syntax in Julia 0.4-pre

    Version 0.10.0 (August 31, 2015)

    • Support (on Julia 0.4 and later) for conditions in indexing @defVar and @addConstraint constructs, for example, @defVar(m, x[i=1:5,j=1:5; i+j >= 3])
    • Support for vectorized operations on Variables and expressions. See the documentation for details.
    • New getVar() method to access variables in a model by name
    • Support for semidefinite programming.
    • Dual solutions are now available for general nonlinear problems. You may call getDual on a reference object for a nonlinear constraint, and getDual on a variable object for Lagrange multipliers from active bounds.
    • Introduce warnings for two common performance traps: too many calls to getValue() on a collection of variables and use of the + operator in a loop to sum expressions.
    • Second-order cone constraints can be written directly with the norm() and norm2{} syntax.
    • Implement MathProgBase interface for querying Hessian-vector products.
    • Iteration over JuMPContainers is deprecated; instead, use the keys and values functions, and zip(keys(d),values(d)) for the old behavior.
    • @defVar returns Array{Variable,N} when each of N index sets are of the form 1:nᵢ.
    • Module precompilation: on Julia 0.4 and later, using JuMP is now much faster.

    Version 0.9.3 (August 11, 2015)

    • Fixes for FactCheck testing on julia v0.4.

    Version 0.9.2 (June 27, 2015)

    • Fix bug in @addConstraints.

    Version 0.9.1 (April 25, 2015)

    • Fix for Julia 0.4-dev.
    • Small infrastructure improvements for extensions.

    Version 0.9.0 (April 18, 2015)

    • Comparison operators for constructing constraints (for example, 2x >= 1) have been deprecated. Instead, construct the constraints explicitly in the @addConstraint macro to add them to the model, or in the @LinearConstraint macro to create a stand-alone linear constraint instance.
    • getValue() method implemented to compute the value of a nonlinear subexpression
    • JuMP is now released under the Mozilla Public License version 2.0 (was previously LGPL). MPL is a copyleft license which is less restrictive than LGPL, especially for embedding JuMP within other applications.
    • A number of performance improvements in ReverseDiffSparse for computing derivatives.
    • MathProgBase.getsolvetime(m) now returns the solution time reported by the solver, if available. (Thanks @odow, Oscar Dowson)
    • Formatting fix for LP format output. (Thanks @sbebo, Leonardo Taccari).

    Version 0.8.0 (February 17, 2015)

    • Nonlinear subexpressions now supported with the @defNLExpr macro.
    • SCS supported for solving second-order conic problems.
    • setXXXCallback family deprecated in favor of addXXXCallback.
    • Multiple callbacks of the same type can be registered.
    • Added support for informational callbacks via addInfoCallback.
    • A CallbackAbort exception can be thrown from callback to safely exit optimization.

    Version 0.7.4 (February 4, 2015)

    • Reduced costs and linear constraint duals are now accessible when quadratic constraints are present.
    • Two-sided nonlinear constraints are supported.
    • Methods for accessing the number of variables and constraints in a model are renamed.
    • New default procedure for setting initial values in nonlinear optimization: project zero onto the variable bounds.
    • Small bug fixes.

    Version 0.7.3 (January 14, 2015)

    • Fix a method ambiguity conflict with Compose.jl (cosmetic fix)

    Version 0.7.2 (January 9, 2015)

    • Fix a bug in sum(::JuMPDict)
    • Added the setCategory function to change a variables category (for example, continuous or binary)

    after construction, and getCategory to retrieve the variable category.

    Version 0.7.1 (January 2, 2015)

    • Fix a bug in parsing linear expressions in macros. Affects only Julia 0.4 and later.

    Version 0.7.0 (December 29, 2014)

    Linear/quadratic/conic programming

    • Breaking change: The syntax for column-wise model generation has been changed to use keyword arguments in @defVar.
    • On Julia 0.4 and later, variables and coefficients may be multiplied in any order within macros. That is, variable*coefficient is now valid syntax.
    • ECOS supported for solving second-order conic problems.

    Nonlinear programming

    • Support for skipping model generation when solving a sequence of nonlinear models with changing data.
    • Fix a memory leak when solving a sequence of nonlinear models.
    • The @addNLConstraint macro now supports the three-argument version to define sets of nonlinear constraints.
    • KNITRO supported as a nonlinear solver.
    • Speed improvements for model generation.
    • The @addNLConstraints macro supports adding multiple (groups of) constraints at once. Syntax is similar to @addConstraints.
    • Discrete variables allowed in nonlinear problems for solvers which support them (currently only KNITRO).

    General

    • Starting values for variables may now be specified with @defVar(m, x, start=value).
    • The setSolver function allows users to change the solver subsequent to model creation.
    • Support for "fixed" variables via the @defVar(m, x == 1) syntax.
    • Unit tests rewritten to use FactCheck.jl, improved testing across solvers.

    Version 0.6.3 (October 19, 2014)

    • Fix a bug in multiplying two AffExpr objects.

    Version 0.6.2 (October 11, 2014)

    • Further improvements and bug fixes for printing.
    • Fixed a bug in @defExpr.
    • Support for accessing expression graphs through the MathProgBase NLP interface.

    Version 0.6.1 (September 19, 2014)

    • Improvements and bug fixes for printing.

    Version 0.6.0 (September 9, 2014)

    • Julia 0.3.0 is the minimum required version for this release.
    • buildInternalModel(m::Model) added to build solver-level model in memory without optimizing.
    • Deprecate load_model_only keyword argument to solve.
    • Add groups of constraints with @addConstraints macro.
    • Unicode operators now supported, including ∑ for sum, ∏ for prod, and ≤/≥
    • Quadratic constraints supported in @addConstraint macro.
    • Quadratic objectives supported in @setObjective macro.
    • MathProgBase solver-independent interface replaces Ipopt-specific interface for nonlinear problems
      • Breaking change: IpoptOptions no longer supported to specify solver options, use m = Model(solver=IpoptSolver(options...)) instead.
    • New solver interfaces: ECOS, NLopt, and nonlinear support for MOSEK
    • New option to control whether the lazy constraint callback is executed at each node in the B&B tree or just when feasible solutions are found
    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
    • Add support for index dependencies (for example, triangular indexing) in @defVar, @addConstraint, and @defExpr (for example, @defVar(m, x[i=1:10,j=i:10])).
      • This required some changes to the internal structure of JuMP containers, which may break code that explicitly stored JuMPDict objects.

    Version 0.5.8 (September 24, 2014)

    • Fix a bug with specifying solvers (affects Julia 0.2 only)

    Version 0.5.7 (September 5, 2014)

    • Fix a bug in printing models

    Version 0.5.6 (September 2, 2014)

    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
      • Breaking change: Syntax for Variable() constructor has changed (use of this interface remains discouraged)
    • Update for breaking changes in MathProgBase

    Version 0.5.5 (July 6, 2014)

    • Fix bug with problem modification: adding variables that did not appear in existing constraints or objective.

    Version 0.5.4 (June 19, 2014)

    • Update for breaking change in MathProgBase which reduces loading times for using JuMP
    • Fix error when MIPs not solved to optimality

    Version 0.5.3 (May 21, 2014)

    • Update for breaking change in ReverseDiffSparse

    Version 0.5.2 (May 9, 2014)

    • Fix compatibility with Julia 0.3 prerelease

    Version 0.5.1 (May 5, 2014)

    • Fix a bug in coefficient handling inside lazy constraints and user cuts

    Version 0.5.0 (May 2, 2014)

    • Support for nonlinear optimization with exact, sparse second-order derivatives automatically computed. Ipopt is currently the only solver supported.
    • getValue for AffExpr and QuadExpr
    • Breaking change: getSolverModel replaced by getInternalModel, which returns the internal MathProgBase-level model
    • Groups of constraints can be specified with @addConstraint (see documentation for details). This is not a breaking change.
    • dot(::JuMPDict{Variable},::JuMPDict{Variable}) now returns the corresponding quadratic expression.

    Version 0.4.1 (March 24, 2014)

    • Fix bug where change in objective sense was ignored when re-solving a model.
    • Fix issue with handling zero coefficients in AffExpr.

    Version 0.4.0 (March 10, 2014)

    • Support for SOS1 and SOS2 constraints.
    • Solver-independent callback for user heuristics.
    • dot and sum implemented for JuMPDict objects. Now you can say @addConstraint(m, dot(a,x) <= b).
    • Developers: support for extensions to JuMP. See definition of Model in src/JuMP.jl for more details.
    • Option to construct the low-level model before optimizing.

    Version 0.3.2 (February 17, 2014)

    • Improved model printing
      • Preliminary support for IJulia output

    Version 0.3.1 (January 30, 2014)

    • Documentation updates
    • Support for MOSEK
    • CPLEXLink renamed to CPLEX

    Version 0.3.0 (January 21, 2014)

    • Unbounded/infeasibility rays: getValue() will return the corresponding components of an unbounded ray when a model is unbounded, if supported by the selected solver. getDual() will return an infeasibility ray (Farkas proof) if a model is infeasible and the selected solver supports this feature.
    • Solver-independent callbacks for user generated cuts.
    • Use new interface for solver-independent QCQP.
    • setlazycallback renamed to setLazyCallback for consistency.

    Version 0.2.0 (December 15, 2013)

    Breaking

    • Objective sense is specified in setObjective instead of in the Model constructor.
    • lpsolver and mipsolver merged into single solver option.

    Added

    • Problem modification with efficient LP restarts and MIP warm-starts.
    • Relatedly, column-wise modeling now supported.
    • Solver-independent callbacks supported. Currently we support only a "lazy constraint" callback, which works with Gurobi, CPLEX, and GLPK. More callbacks coming soon.

    Version 0.1.2 (November 16, 2013)

    • Bug fixes for printing, improved error messages.
    • Allow AffExpr to be used in macros; for example, ex = y + z; @addConstraint(m, x + 2*ex <= 3)

    Version 0.1.1 (October 23, 2013)

    • Update for solver specification API changes in MathProgBase.

    Version 0.1.0 (October 3, 2013)

    • Initial public release.
    +end

  • The lowerbound, upperbound, and basename keyword arguments to the @variable macro have been renamed to lower_bound, upper_bound, and base_name, for consistency with JuMP's new style recommendations.

  • We rely on broadcasting syntax to apply accessors to collections of variables, for example, value.(x) instead of getvalue(x) for collections. (Use value(x) when x is a scalar object.)

    • Added

    • Splatting (like f(x...)) is recognized in restricted settings in nonlinear expressions.

    • Support for deleting constraints and variables.

    • The documentation has been completely rewritten using docstrings and Documenter.

    • Support for modeling mixed conic and quadratic models (for example, conic models with quadratic objectives and bi-linear matrix inequalities).

    • Significantly improved support for modeling new types of constraints and for extending JuMP's macros.

    • Support for providing dual warm starts.

    • Improved support for accessing solver-specific attributes (for example, the irreducible inconsistent subsystem).

    • Explicit control of whether symmetry-enforcing constraints are added to PSD constraints.

    • Support for modeling exponential cones.

    • Significant improvements in internal code quality and testing.

    • Style and naming guidelines.

    • Direct mode and manual mode provide explicit control over when copies of a model are stored or regenerated. See the corresponding documentation.

    Regressions

    There are known regressions from JuMP 0.18 that will be addressed in a future release (0.19.x or later):

    • Performance regressions in model generation (issue). Please file an issue anyway if you notice a significant performance regression. We have plans to address a number of performance issues, but we might not be aware of all of them.

    • Fast incremental NLP solves are not yet reimplemented (issue).

    • We do not yet have an implementation of solver-specific callbacks.

    • The column generation syntax in @variable has been removed (that is, the objective, coefficients, and inconstraints keyword arguments). Support for column generation will be re-introduced in a future release.

    • The ability to solve the continuous relaxation (that is, via solve(model; relaxation = true)) is not yet reimplemented (issue).

    Version 0.18.5 (December 1, 2018)

    • Support views in some derivative evaluation functions.
    • Improved compatibility with PackageCompiler.

    Version 0.18.4 (October 8, 2018)

    • Fix a bug in model printing on Julia 0.7 and 1.0.

    Version 0.18.3 (October 1, 2018)

    • Add support for Julia v1.0 (Thanks @ExpandingMan)
    • Fix matrix expressions with quadratic functions (#1508)

    Version 0.18.2 (June 10, 2018)

    • Fix a bug in second-order derivatives when expressions are present (#1319)
    • Fix a bug in @constraintref (#1330)

    Version 0.18.1 (April 9, 2018)

    • Fix for nested tuple destructuring (#1193)
    • Preserve internal model when relaxation=true (#1209)
    • Minor bug fixes and updates for example

    Version 0.18.0 (July 27, 2017)

    • Drop support for Julia 0.5.
    • Update for ForwardDiff 0.5.
    • Minor bug fixes.

    Version 0.17.1 (June 9, 2017)

    • Use of constructconstraint! in @SDconstraint.
    • Minor bug fixes.

    Version 0.17.0 (May 27, 2017)

    • Breaking change: Mixing quadratic and conic constraints is no longer supported.
    • Breaking change: The getvariable and getconstraint functions are replaced by indexing on the corresponding symbol. For instance, to access the variable with name x, one should now write m[:x] instead of getvariable(m, :x). As a consequence, creating a variable and constraint with the same name now triggers a warning, and accessing one of them afterwards throws an error. This change is breaking only in the latter case.
    • Addition of the getobjectivebound function that mirrors the functionality of the MathProgBase getobjbound function except that it takes into account transformations performed by JuMP.
    • Minor bug fixes.

    The following changes are primarily of interest to developers of JuMP extensions:

    • The new syntax @constraint(model, expr in Cone) creates the constraint ensuring that expr is inside Cone. The Cone argument is passed to constructconstraint! which enables the call to the dispatched to an extension.
    • The @variable macro now calls constructvariable! instead of directly calling the Variable constructor. Extra arguments and keyword arguments passed to @variable are passed to constructvariable! which enables the call to be dispatched to an extension.
    • Refactor the internal function conicdata (used build the MathProgBase conic model) into smaller sub-functions to make these parts reusable by extensions.

    Version 0.16.2 (March 28, 2017)

    • Minor bug fixes and printing tweaks
    • Address deprecation warnings for Julia 0.6

    Version 0.16.1 (March 7, 2017)

    • Better support for AbstractArray in JuMP (Thanks @tkoolen)
    • Minor bug fixes

    Version 0.16.0 (February 23, 2017)

    • Breaking change: JuMP no longer has a mechanism for selecting solvers by default (the previous mechanism was flawed and incompatible with Julia 0.6). Not specifying a solver before calling solve() will result in an error.
    • Breaking change: User-defined functions are no longer global. The first argument to JuMP.register is now a JuMP Model object within whose scope the function will be registered. Calling JuMP.register without a Model now produces an error.
    • Breaking change: Use the new JuMP.fix method to fix a variable to a value or to update the value to which a variable is fixed. Calling setvalue on a fixed variable now results in an error in order to avoid silent behavior changes. (Thanks @joaquimg)
    • Nonlinear expressions now print out similarly to linear/quadratic expressions (useful for debugging!)
    • New category keyword to @variable. Used for specifying categories of anonymous variables.
    • Compatibility with Julia 0.6-dev.
    • Minor fixes and improvements (Thanks @cossio, @ccoffrin, @blegat)

    Version 0.15.1 (January 31, 2017)

    • Bugfix for @LinearConstraints and friends

    Version 0.15.0 (December 22, 2016)

    • Julia 0.5.0 is the minimum required version for this release.
    • Document support for BARON solver
    • Enable info callbacks in more states than before, for example, for recording solutions. New when argument to addinfocallback (#814, thanks @yeesian)
    • Improved support for anonymous variables. This includes new warnings for potentially confusing use of the traditional non-anonymous syntax:
      • When multiple variables in a model are given the same name
      • When non-symbols are used as names, for example, @variable(m, x[1][1:N])
    • Improvements in iterating over JuMP containers (#836, thanks @IssamT)
    • Support for writing variable names in .lp file output (Thanks @leethargo)
    • Support for querying duals to SDP problems (Thanks @blegat)
    • The comprehension syntax with curly braces sum{}, prod{}, and norm2{} has been deprecated in favor of Julia's native comprehension syntax sum(), prod() and norm() as previously announced. (For early adopters of the new syntax, norm2() was renamed to norm() without deprecation.)
    • Unit tests rewritten to use Base.Test instead of FactCheck
    • Improved support for operations with matrices of JuMP types (Thanks @ExpandingMan)
    • The syntax to halt a solver from inside a callback has changed from throw(CallbackAbort()) to return JuMP.StopTheSolver
    • Minor bug fixes

    Version 0.14.2 (December 12, 2016)

    • Allow singleton anonymous variables (includes bugfix)

    Version 0.14.1 (September 12, 2016)

    • More consistent handling of states in informational callbacks, includes a new when parameter to addinfocallback for specifying in which state an informational callback should be called.

    Version 0.14.0 (August 7, 2016)

    • Compatibility with Julia 0.5 and ForwardDiff 0.2
    • Support for "anonymous" variables, constraints, expressions, and parameters, for example, x = @variable(m, [1:N]) instead of @variable(m, x[1:N])
    • Support for retrieving constraints from a model by name via getconstraint
    • @NLconstraint now returns constraint references (as expected).
    • Support for vectorized expressions within lazy constraints
    • On Julia 0.5, parse new comprehension syntax sum(x[i] for i in 1:N if isodd(i)) instead of sum{ x[i], i in 1:N; isodd(i) }. The old syntax with curly braces will be deprecated in JuMP 0.15.
    • Now possible to provide nonlinear expressions as "raw" Julia Expr objects instead of using JuMP's nonlinear macros. This input format is useful for programmatically generated expressions.
    • s/Mathematical Programming/Mathematical Optimization/
    • Support for local cuts (Thanks to @madanim, Mehdi Madani)
    • Document Xpress interface developed by @joaquimg, Joaquim Dias Garcia
    • Minor bug and deprecation fixes (Thanks @odow, @jrevels)

    Version 0.13.2 (May 16, 2016)

    • Compatibility update for MathProgBase

    Version 0.13.1 (May 3, 2016)

    • Fix broken deprecation for registerNLfunction.

    Version 0.13.0 (April 29, 2016)

    • Most exported methods and macros have been renamed to avoid camelCase. See the list of changes here. There is a 1-1 mapping from the old names to the new, and it is safe to simply replace the names to update existing models.
    • Specify variable lower/upper bounds in @variable using the lowerbound and upperbound keyword arguments.
    • Change name printed for variable using the basename keyword argument to @variable.
    • New @variables macro allows multi-line declaration of groups of variables.
    • A number of solver methods previously available only through MathProgBase are now exposed directly in JuMP. The fix was recorded live.
    • Compatibility fixes with Julia 0.5.
    • The "end" indexing syntax is no longer supported within JuMPArrays which do not use 1-based indexing until upstream issues are resolved, see here.

    Version 0.12.2 (March 9, 2016)

    • Small fixes for nonlinear optimization

    Version 0.12.1 (March 1, 2016)

    • Fix a regression in slicing for JuMPArrays (when not using 1-based indexing)

    Version 0.12.0 (February 27, 2016)

    • The automatic differentiation functionality has been completely rewritten with a number of user-facing changes:
      • @defExpr and @defNLExpr now take the model as the first argument. The previous one-argument version of @defExpr is deprecated; all expressions should be named. For example, replace @defExpr(2x+y) with @defExpr(jump_model, my_expr, 2x+y).
      • JuMP no longer uses Julia's variable binding rules for efficiently re-solving a sequence of nonlinear models. Instead, we have introduced nonlinear parameters. This is a breaking change, so we have added a warning message when we detect models that may depend on the old behavior.
      • Support for user-defined functions integrated within nonlinear JuMP expressions.
    • Replaced iteration over AffExpr with Number-like scalar iteration; previous iteration behavior is now available via linearterms(::AffExpr).
    • Stopping the solver via throw(CallbackAbort()) from a callback no longer triggers an exception. Instead, solve() returns UserLimit status.
    • getDual() now works for conic problems (Thanks @emreyamangil.)

    Version 0.11.3 (February 4, 2016)

    • Bug-fix for problems with quadratic objectives and semidefinite constraints

    Version 0.11.2 (January 14, 2016)

    • Compatibility update for Mosek

    Version 0.11.1 (December 1, 2015)

    • Remove usage of @compat in tests.
    • Fix updating quadratic objectives for nonlinear models.

    Version 0.11.0 (November 30, 2015)

    • Julia 0.4.0 is the minimum required version for this release.
    • Fix for scoping semantics of index variables in sum{}. Index variables no longer leak into the surrounding scope.
    • Addition of the solve(m::Model, relaxation=true) keyword argument to solve the standard continuous relaxation of model m
    • The getConstraintBounds() method allows access to the lower and upper bounds of all constraints in a (nonlinear) model.
    • Update for breaking changes in MathProgBase

    Version 0.10.3 (November 20, 2015)

    • Fix a rare error when parsing quadratic expressions
    • Fix Variable() constructor with default arguments
    • Detect unrecognized keywords in solve()

    Version 0.10.2 (September 28, 2015)

    • Fix for deprecation warnings

    Version 0.10.1 (September 3, 2015)

    • Fixes for ambiguity warnings.
    • Fix for breaking change in precompilation syntax in Julia 0.4-pre

    Version 0.10.0 (August 31, 2015)

    • Support (on Julia 0.4 and later) for conditions in indexing @defVar and @addConstraint constructs, for example, @defVar(m, x[i=1:5,j=1:5; i+j >= 3])
    • Support for vectorized operations on Variables and expressions. See the documentation for details.
    • New getVar() method to access variables in a model by name
    • Support for semidefinite programming.
    • Dual solutions are now available for general nonlinear problems. You may call getDual on a reference object for a nonlinear constraint, and getDual on a variable object for Lagrange multipliers from active bounds.
    • Introduce warnings for two common performance traps: too many calls to getValue() on a collection of variables and use of the + operator in a loop to sum expressions.
    • Second-order cone constraints can be written directly with the norm() and norm2{} syntax.
    • Implement MathProgBase interface for querying Hessian-vector products.
    • Iteration over JuMPContainers is deprecated; instead, use the keys and values functions, and zip(keys(d),values(d)) for the old behavior.
    • @defVar returns Array{Variable,N} when each of N index sets are of the form 1:nᵢ.
    • Module precompilation: on Julia 0.4 and later, using JuMP is now much faster.

    Version 0.9.3 (August 11, 2015)

    • Fixes for FactCheck testing on julia v0.4.

    Version 0.9.2 (June 27, 2015)

    • Fix bug in @addConstraints.

    Version 0.9.1 (April 25, 2015)

    • Fix for Julia 0.4-dev.
    • Small infrastructure improvements for extensions.

    Version 0.9.0 (April 18, 2015)

    • Comparison operators for constructing constraints (for example, 2x >= 1) have been deprecated. Instead, construct the constraints explicitly in the @addConstraint macro to add them to the model, or in the @LinearConstraint macro to create a stand-alone linear constraint instance.
    • getValue() method implemented to compute the value of a nonlinear subexpression
    • JuMP is now released under the Mozilla Public License version 2.0 (was previously LGPL). MPL is a copyleft license which is less restrictive than LGPL, especially for embedding JuMP within other applications.
    • A number of performance improvements in ReverseDiffSparse for computing derivatives.
    • MathProgBase.getsolvetime(m) now returns the solution time reported by the solver, if available. (Thanks @odow, Oscar Dowson)
    • Formatting fix for LP format output. (Thanks @sbebo, Leonardo Taccari).

    Version 0.8.0 (February 17, 2015)

    • Nonlinear subexpressions now supported with the @defNLExpr macro.
    • SCS supported for solving second-order conic problems.
    • setXXXCallback family deprecated in favor of addXXXCallback.
    • Multiple callbacks of the same type can be registered.
    • Added support for informational callbacks via addInfoCallback.
    • A CallbackAbort exception can be thrown from callback to safely exit optimization.

    Version 0.7.4 (February 4, 2015)

    • Reduced costs and linear constraint duals are now accessible when quadratic constraints are present.
    • Two-sided nonlinear constraints are supported.
    • Methods for accessing the number of variables and constraints in a model are renamed.
    • New default procedure for setting initial values in nonlinear optimization: project zero onto the variable bounds.
    • Small bug fixes.

    Version 0.7.3 (January 14, 2015)

    • Fix a method ambiguity conflict with Compose.jl (cosmetic fix)

    Version 0.7.2 (January 9, 2015)

    • Fix a bug in sum(::JuMPDict)
    • Added the setCategory function to change a variables category (for example, continuous or binary)

    after construction, and getCategory to retrieve the variable category.

    Version 0.7.1 (January 2, 2015)

    • Fix a bug in parsing linear expressions in macros. Affects only Julia 0.4 and later.

    Version 0.7.0 (December 29, 2014)

    Linear/quadratic/conic programming

    • Breaking change: The syntax for column-wise model generation has been changed to use keyword arguments in @defVar.
    • On Julia 0.4 and later, variables and coefficients may be multiplied in any order within macros. That is, variable*coefficient is now valid syntax.
    • ECOS supported for solving second-order conic problems.

    Nonlinear programming

    • Support for skipping model generation when solving a sequence of nonlinear models with changing data.
    • Fix a memory leak when solving a sequence of nonlinear models.
    • The @addNLConstraint macro now supports the three-argument version to define sets of nonlinear constraints.
    • KNITRO supported as a nonlinear solver.
    • Speed improvements for model generation.
    • The @addNLConstraints macro supports adding multiple (groups of) constraints at once. Syntax is similar to @addConstraints.
    • Discrete variables allowed in nonlinear problems for solvers which support them (currently only KNITRO).

    General

    • Starting values for variables may now be specified with @defVar(m, x, start=value).
    • The setSolver function allows users to change the solver subsequent to model creation.
    • Support for "fixed" variables via the @defVar(m, x == 1) syntax.
    • Unit tests rewritten to use FactCheck.jl, improved testing across solvers.

    Version 0.6.3 (October 19, 2014)

    • Fix a bug in multiplying two AffExpr objects.

    Version 0.6.2 (October 11, 2014)

    • Further improvements and bug fixes for printing.
    • Fixed a bug in @defExpr.
    • Support for accessing expression graphs through the MathProgBase NLP interface.

    Version 0.6.1 (September 19, 2014)

    • Improvements and bug fixes for printing.

    Version 0.6.0 (September 9, 2014)

    • Julia 0.3.0 is the minimum required version for this release.
    • buildInternalModel(m::Model) added to build solver-level model in memory without optimizing.
    • Deprecate load_model_only keyword argument to solve.
    • Add groups of constraints with @addConstraints macro.
    • Unicode operators now supported, including ∑ for sum, ∏ for prod, and ≤/≥
    • Quadratic constraints supported in @addConstraint macro.
    • Quadratic objectives supported in @setObjective macro.
    • MathProgBase solver-independent interface replaces Ipopt-specific interface for nonlinear problems
      • Breaking change: IpoptOptions no longer supported to specify solver options, use m = Model(solver=IpoptSolver(options...)) instead.
    • New solver interfaces: ECOS, NLopt, and nonlinear support for MOSEK
    • New option to control whether the lazy constraint callback is executed at each node in the B&B tree or just when feasible solutions are found
    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
    • Add support for index dependencies (for example, triangular indexing) in @defVar, @addConstraint, and @defExpr (for example, @defVar(m, x[i=1:10,j=i:10])).
      • This required some changes to the internal structure of JuMP containers, which may break code that explicitly stored JuMPDict objects.

    Version 0.5.8 (September 24, 2014)

    • Fix a bug with specifying solvers (affects Julia 0.2 only)

    Version 0.5.7 (September 5, 2014)

    • Fix a bug in printing models

    Version 0.5.6 (September 2, 2014)

    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
      • Breaking change: Syntax for Variable() constructor has changed (use of this interface remains discouraged)
    • Update for breaking changes in MathProgBase

    Version 0.5.5 (July 6, 2014)

    • Fix bug with problem modification: adding variables that did not appear in existing constraints or objective.

    Version 0.5.4 (June 19, 2014)

    • Update for breaking change in MathProgBase which reduces loading times for using JuMP
    • Fix error when MIPs not solved to optimality

    Version 0.5.3 (May 21, 2014)

    • Update for breaking change in ReverseDiffSparse

    Version 0.5.2 (May 9, 2014)

    • Fix compatibility with Julia 0.3 prerelease

    Version 0.5.1 (May 5, 2014)

    • Fix a bug in coefficient handling inside lazy constraints and user cuts

    Version 0.5.0 (May 2, 2014)

    • Support for nonlinear optimization with exact, sparse second-order derivatives automatically computed. Ipopt is currently the only solver supported.
    • getValue for AffExpr and QuadExpr
    • Breaking change: getSolverModel replaced by getInternalModel, which returns the internal MathProgBase-level model
    • Groups of constraints can be specified with @addConstraint (see documentation for details). This is not a breaking change.
    • dot(::JuMPDict{Variable},::JuMPDict{Variable}) now returns the corresponding quadratic expression.

    Version 0.4.1 (March 24, 2014)

    • Fix bug where change in objective sense was ignored when re-solving a model.
    • Fix issue with handling zero coefficients in AffExpr.

    Version 0.4.0 (March 10, 2014)

    • Support for SOS1 and SOS2 constraints.
    • Solver-independent callback for user heuristics.
    • dot and sum implemented for JuMPDict objects. Now you can say @addConstraint(m, dot(a,x) <= b).
    • Developers: support for extensions to JuMP. See definition of Model in src/JuMP.jl for more details.
    • Option to construct the low-level model before optimizing.

    Version 0.3.2 (February 17, 2014)

    • Improved model printing
      • Preliminary support for IJulia output

    Version 0.3.1 (January 30, 2014)

    • Documentation updates
    • Support for MOSEK
    • CPLEXLink renamed to CPLEX

    Version 0.3.0 (January 21, 2014)

    • Unbounded/infeasibility rays: getValue() will return the corresponding components of an unbounded ray when a model is unbounded, if supported by the selected solver. getDual() will return an infeasibility ray (Farkas proof) if a model is infeasible and the selected solver supports this feature.
    • Solver-independent callbacks for user generated cuts.
    • Use new interface for solver-independent QCQP.
    • setlazycallback renamed to setLazyCallback for consistency.

    Version 0.2.0 (December 15, 2013)

    Breaking

    • Objective sense is specified in setObjective instead of in the Model constructor.
    • lpsolver and mipsolver merged into single solver option.

    Added

    • Problem modification with efficient LP restarts and MIP warm-starts.
    • Relatedly, column-wise modeling now supported.
    • Solver-independent callbacks supported. Currently we support only a "lazy constraint" callback, which works with Gurobi, CPLEX, and GLPK. More callbacks coming soon.

    Version 0.1.2 (November 16, 2013)

    • Bug fixes for printing, improved error messages.
    • Allow AffExpr to be used in macros; for example, ex = y + z; @addConstraint(m, x + 2*ex <= 3)

    Version 0.1.1 (October 23, 2013)

    • Update for solver specification API changes in MathProgBase.

    Version 0.1.0 (October 3, 2013)

    • Initial public release.
    diff --git a/previews/PR3913/developers/checklists/index.html b/previews/PR3913/developers/checklists/index.html index 07d9d34e7ff..05116bef569 100644 --- a/previews/PR3913/developers/checklists/index.html +++ b/previews/PR3913/developers/checklists/index.html @@ -69,4 +69,4 @@ - [ ] Implement `vectorize(data, ::NewShape)::Vector` - [ ] Implement `reshape_vector(vector, ::NewShape)` - [ ] Implement `dual_shape`, or verify that the shape is self-dual - - [ ] Add the tests from https://github.com/jump-dev/JuMP.jl/pull/3816 + - [ ] Add the tests from https://github.com/jump-dev/JuMP.jl/pull/3816 diff --git a/previews/PR3913/developers/contributing/index.html b/previews/PR3913/developers/contributing/index.html index 84382a30b2e..d1aa2eeb229 100644 --- a/previews/PR3913/developers/contributing/index.html +++ b/previews/PR3913/developers/contributing/index.html @@ -25,4 +25,4 @@ $ git checkout master -$ git pull
    Note

    If you have suggestions to improve this guide, please make a pull request. It's particularly helpful if you do this after your first pull request because you'll know all the parts that could be explained better.

    +$ git pull
    Note

    If you have suggestions to improve this guide, please make a pull request. It's particularly helpful if you do this after your first pull request because you'll know all the parts that could be explained better.

    diff --git a/previews/PR3913/developers/custom_solver_binaries/index.html b/previews/PR3913/developers/custom_solver_binaries/index.html index b2ed23d5daf..4f0bf96d8f7 100644 --- a/previews/PR3913/developers/custom_solver_binaries/index.html +++ b/previews/PR3913/developers/custom_solver_binaries/index.html @@ -90,4 +90,4 @@ libCbc_path = "/usr/local/Cellar/cbc/2.10.5/lib/libCbc.3.10.5" libOsiCbc_path = "/usr/local/Cellar/cbc/2.10.5/lib/libOsiCbc.3.10.5" libcbcsolver_path = "/usr/local/Cellar/cbc/2.10.5/lib/libCbcSolver.3.10.5"
    Info

    Note that capitalization matters, so libcbcsolver_path corresponds to libCbcSolver.3.10.5.

    Override entire artifact

    To use the homebrew install as our custom binary we add the following to ~/.julia/artifacts/Overrides.toml:

    # Override for Cbc_jll
-e481bc81db5e229ba1f52b2b4bd57484204b1b06 = "/usr/local/Cellar/cbc/2.10.5"
    +e481bc81db5e229ba1f52b2b4bd57484204b1b06 = "/usr/local/Cellar/cbc/2.10.5" diff --git a/previews/PR3913/developers/extensions/index.html b/previews/PR3913/developers/extensions/index.html index 3093193e784..cfa5d54be3b 100644 --- a/previews/PR3913/developers/extensions/index.html +++ b/previews/PR3913/developers/extensions/index.html @@ -310,4 +310,4 @@ _function_barrier(names, model, F, S) end return names -end
    Note

    It is important to explicitly type the F and S arguments. If you leave them untyped, for example, function _function_barrier(names, model, F, S), Julia will not specialize the function calls and performance will not be improved.

    +end
    Note

    It is important to explicitly type the F and S arguments. If you leave them untyped, for example, function _function_barrier(names, model, F, S), Julia will not specialize the function calls and performance will not be improved.

    diff --git a/previews/PR3913/developers/roadmap/index.html b/previews/PR3913/developers/roadmap/index.html index 095000b3085..ced02270632 100644 --- a/previews/PR3913/developers/roadmap/index.html +++ b/previews/PR3913/developers/roadmap/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Development roadmap

    The JuMP developers have compiled this roadmap document to share their plans and goals with the JuMP community. Contributions to roadmap issues are especially invited.

    Most of these issues will require changes to both JuMP and MathOptInterface, and are non-trivial in their implementation. They are in no particular order, but represent broad themes that we see as areas in which JuMP could be improved.

    • Support nonlinear expressions with vector-valued inputs and outputs. There are a few related components:
      • Representing terms like log(det(X)) as necessary for Convex.jl
      • Automatic differentiation of terms with vector inputs and outputs
      • User-defined functions with vector–as opposed to scalar–inputs, which is particularly useful for optimal control problems
      • User-defined functions with vector outputs, avoiding the need for User-defined operators with vector outputs
    • Add support for modeling with SI units. The UnitJuMP.jl extension is a good proof of concept for what this would look like. We want to make units a first-class concept in JuMP. See #1350 for more details.

    Completed

    +
    GitHub

    Development roadmap

    The JuMP developers have compiled this roadmap document to share their plans and goals with the JuMP community. Contributions to roadmap issues are especially invited.

    Most of these issues will require changes to both JuMP and MathOptInterface, and are non-trivial in their implementation. They are in no particular order, but represent broad themes that we see as areas in which JuMP could be improved.

    • Support nonlinear expressions with vector-valued inputs and outputs. There are a few related components:
      • Representing terms like log(det(X)) as necessary for Convex.jl
      • Automatic differentiation of terms with vector inputs and outputs
      • User-defined functions with vector–as opposed to scalar–inputs, which is particularly useful for optimal control problems
      • User-defined functions with vector outputs, avoiding the need for User-defined operators with vector outputs
    • Add support for modeling with SI units. The UnitJuMP.jl extension is a good proof of concept for what this would look like. We want to make units a first-class concept in JuMP. See #1350 for more details.

    Completed

    diff --git a/previews/PR3913/developers/style/index.html b/previews/PR3913/developers/style/index.html index 74e5005fab2..0b88b46cf2a 100644 --- a/previews/PR3913/developers/style/index.html +++ b/previews/PR3913/developers/style/index.html @@ -182,4 +182,4 @@ end # module TestPkg -TestPkg.runtests()

    Break the tests into multiple files, with one module per file, so that subsets of the codebase can be tested by calling include with the relevant file.

    +TestPkg.runtests()

    Break the tests into multiple files, with one module per file, so that subsets of the codebase can be tested by calling include with the relevant file.

    diff --git a/previews/PR3913/extensions/DimensionalData/index.html b/previews/PR3913/extensions/DimensionalData/index.html index c883922b3ad..f89d35d2112 100644 --- a/previews/PR3913/extensions/DimensionalData/index.html +++ b/previews/PR3913/extensions/DimensionalData/index.html @@ -45,4 +45,4 @@ ↓ j Categorical{String} ["a", "b"] ForwardOrdered └──────────────────────────────────────────────────────────────────────────────┘ "a" x[2,a] + x[3,a] + x[4,a] ≤ 1 - "b" x[2,b] + x[3,b] + x[4,b] ≤ 1

    Documentation

    See the DimensionalData.jl documentation for more details on the syntax and features of DimensionalData.DimArray.

    + "b" x[2,b] + x[3,b] + x[4,b] ≤ 1

    Documentation

    See the DimensionalData.jl documentation for more details on the syntax and features of DimensionalData.DimArray.

    diff --git a/previews/PR3913/extensions/introduction/index.html b/previews/PR3913/extensions/introduction/index.html index 12602cb5c57..28380933c33 100644 --- a/previews/PR3913/extensions/introduction/index.html +++ b/previews/PR3913/extensions/introduction/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Introduction

    This section of the documentation contains brief documentation for some popular JuMP extensions. The list of extensions is not exhaustive, but instead is intended to help you discover popular JuMP extensions, and to give you an overview of the types of extensions that are possible to write with JuMP.

    Affiliation

    Packages beginning with jump-dev/ are developed and maintained by the JuMP developers.

    Packages that do not begin with jump-dev/ are developed independently. The developers of these packages requested or consented to the inclusion of their README contents in the JuMP documentation for the benefit of users.

    Adding new extensions

    Written an extension? Add it to this section of the JuMP documentation by making a pull request to the docs/packages.toml file.

    Weak dependencies

    Some extensions listed in this section are implemented using the weak dependency feature added to Julia in v1.9. These extensions are activated if and only if you have JuMP and the other package loaded into your current scope with using or import.

    Compat

    Using a weak dependency requires Julia v1.9 or later.

    +
    GitHub

    Introduction

    This section of the documentation contains brief documentation for some popular JuMP extensions. The list of extensions is not exhaustive, but instead is intended to help you discover popular JuMP extensions, and to give you an overview of the types of extensions that are possible to write with JuMP.

    Affiliation

    Packages beginning with jump-dev/ are developed and maintained by the JuMP developers.

    Packages that do not begin with jump-dev/ are developed independently. The developers of these packages requested or consented to the inclusion of their README contents in the JuMP documentation for the benefit of users.

    Adding new extensions

    Written an extension? Add it to this section of the JuMP documentation by making a pull request to the docs/packages.toml file.

    Weak dependencies

    Some extensions listed in this section are implemented using the weak dependency feature added to Julia in v1.9. These extensions are activated if and only if you have JuMP and the other package loaded into your current scope with using or import.

    Compat

    Using a weak dependency requires Julia v1.9 or later.

    diff --git a/previews/PR3913/index.html b/previews/PR3913/index.html index c70b1148c2e..dda2d54eec8 100644 --- a/previews/PR3913/index.html +++ b/previews/PR3913/index.html @@ -32,4 +32,4 @@ journal = {Mathematical Programming Computation}, year = {2023}, doi = {10.1007/s12532-023-00239-3} -}

    NumFOCUS

    NumFOCUS logo

    JuMP is a Sponsored Project of NumFOCUS, a 501(c)(3) nonprofit charity in the United States. NumFOCUS provides JuMP with fiscal, legal, and administrative support to help ensure the health and sustainability of the project. Visit numfocus.org for more information.

    You can support JuMP by donating.

    Donations to JuMP are managed by NumFOCUS. For donors in the United States, your gift is tax-deductible to the extent provided by law. As with any donation, you should consult with your tax adviser about your particular tax situation.

    JuMP's largest expense is the annual JuMP-dev workshop. Donations will help us provide travel support for JuMP-dev attendees and take advantage of other opportunities that arise to support JuMP development.

    License

    JuMP is licensed under the MPL-2.0 software license. Consult the license and the Mozilla FAQ for more information. In addition, JuMP is typically used in conjunction with solver packages and extensions which have their own licences. Consult their package repositories for the specific licenses that apply.

    +}

    NumFOCUS

    NumFOCUS logo

    JuMP is a Sponsored Project of NumFOCUS, a 501(c)(3) nonprofit charity in the United States. NumFOCUS provides JuMP with fiscal, legal, and administrative support to help ensure the health and sustainability of the project. Visit numfocus.org for more information.

    You can support JuMP by donating.

    Donations to JuMP are managed by NumFOCUS. For donors in the United States, your gift is tax-deductible to the extent provided by law. As with any donation, you should consult with your tax adviser about your particular tax situation.

    JuMP's largest expense is the annual JuMP-dev workshop. Donations will help us provide travel support for JuMP-dev attendees and take advantage of other opportunities that arise to support JuMP development.

    License

    JuMP is licensed under the MPL-2.0 software license. Consult the license and the Mozilla FAQ for more information. In addition, JuMP is typically used in conjunction with solver packages and extensions which have their own licences. Consult their package repositories for the specific licenses that apply.

    diff --git a/previews/PR3913/installation/index.html b/previews/PR3913/installation/index.html index c156d5c3c30..c197d30fcaa 100644 --- a/previews/PR3913/installation/index.html +++ b/previews/PR3913/installation/index.html @@ -28,4 +28,4 @@ [4076af6c] ↓ JuMP v0.21.5 ⇒ v0.18.6 [707a9f91] + JuMPeR v0.6.0 Updating `~/jump_example/Manifest.toml` - ... lines omitted ...

    JuMPeR gets added at version 0.6.0 (+ JuMPeR v0.6.0), but JuMP gets downgraded from 0.21.5 to 0.18.6 (↓ JuMP v0.21.5 ⇒ v0.18.6)! The reason for this is that JuMPeR doesn't support a version of JuMP newer than 0.18.6.

    Tip

    Pay careful attention to the output of the package manager when adding new packages, especially when you see a package being downgraded.

    + ... lines omitted ...

    JuMPeR gets added at version 0.6.0 (+ JuMPeR v0.6.0), but JuMP gets downgraded from 0.21.5 to 0.18.6 (↓ JuMP v0.21.5 ⇒ v0.18.6)! The reason for this is that JuMPeR doesn't support a version of JuMP newer than 0.18.6.

    Tip

    Pay careful attention to the output of the package manager when adding new packages, especially when you see a package being downgraded.

    diff --git a/previews/PR3913/manual/callbacks/index.html b/previews/PR3913/manual/callbacks/index.html index 237cb35ff6f..f4949132e01 100644 --- a/previews/PR3913/manual/callbacks/index.html +++ b/previews/PR3913/manual/callbacks/index.html @@ -81,4 +81,4 @@ end my_callback_function (generic function with 1 method) -julia> set_attribute(model, MOI.HeuristicCallback(), my_callback_function)

    The third argument to submit is a vector of JuMP variables, and the fourth argument is a vector of values corresponding to each variable.

    MOI.submit returns an enum that depends on whether the solver accepted the solution. The possible return codes are:

    • MOI.HEURISTIC_SOLUTION_ACCEPTED
    • MOI.HEURISTIC_SOLUTION_REJECTED
    • MOI.HEURISTIC_SOLUTION_UNKNOWN
    Warning

    Some solvers may accept partial solutions. Others require a feasible integer solution for every variable. If in doubt, provide a complete solution.

    Info

    The heuristic solution callback may be called at fractional nodes in the branch-and-bound tree. There is no guarantee that the callback is called at every fractional primal solution.

    +julia> set_attribute(model, MOI.HeuristicCallback(), my_callback_function)

    The third argument to submit is a vector of JuMP variables, and the fourth argument is a vector of values corresponding to each variable.

    MOI.submit returns an enum that depends on whether the solver accepted the solution. The possible return codes are:

    • MOI.HEURISTIC_SOLUTION_ACCEPTED
    • MOI.HEURISTIC_SOLUTION_REJECTED
    • MOI.HEURISTIC_SOLUTION_UNKNOWN
    Warning

    Some solvers may accept partial solutions. Others require a feasible integer solution for every variable. If in doubt, provide a complete solution.

    Info

    The heuristic solution callback may be called at fractional nodes in the branch-and-bound tree. There is no guarantee that the callback is called at every fractional primal solution.

    diff --git a/previews/PR3913/manual/complex/index.html b/previews/PR3913/manual/complex/index.html index 533c592ea7c..e63aaf38c67 100644 --- a/previews/PR3913/manual/complex/index.html +++ b/previews/PR3913/manual/complex/index.html @@ -197,4 +197,4 @@ julia> @constraint(model, H in HermitianPSDCone()) [x[1] im - -im -x[2]] ∈ HermitianPSDCone()
    Note

    The matrix H in H in HermitianPSDCone() must be a LinearAlgebra.Hermitian matrix type. A build_constraint error will be thrown if the matrix is a different matrix type.

    + -im -x[2]] ∈ HermitianPSDCone()
    Note

    The matrix H in H in HermitianPSDCone() must be a LinearAlgebra.Hermitian matrix type. A build_constraint error will be thrown if the matrix is a different matrix type.

    diff --git a/previews/PR3913/manual/constraints/index.html b/previews/PR3913/manual/constraints/index.html index 0239c396ddc..706d17d95b9 100644 --- a/previews/PR3913/manual/constraints/index.html +++ b/previews/PR3913/manual/constraints/index.html @@ -801,4 +801,4 @@ (x[1] == x[2]) - 0.0 = 0 julia> @constraint(model, x[1] == x[2] := rhs) -x[1] == x[2] = false +x[1] == x[2] = false diff --git a/previews/PR3913/manual/containers/index.html b/previews/PR3913/manual/containers/index.html index 08aa378c836..5473d7e7419 100644 --- a/previews/PR3913/manual/containers/index.html +++ b/previews/PR3913/manual/containers/index.html @@ -232,4 +232,4 @@ julia> Containers.@container([i = 1:2, j = 1:4; condition(i, j)], i + j) JuMP.Containers.SparseAxisArray{Int64, 2, Tuple{Int64, Int64}} with 2 entries: [1, 2] = 3 - [1, 4] = 5 + [1, 4] = 5 diff --git a/previews/PR3913/manual/expressions/index.html b/previews/PR3913/manual/expressions/index.html index 11ceb1c9737..6c9ee820106 100644 --- a/previews/PR3913/manual/expressions/index.html +++ b/previews/PR3913/manual/expressions/index.html @@ -247,4 +247,4 @@ julia> x 2-element Vector{AffExpr}: 1.1 - 0

    Note that for large expressions this will be slower due to the allocation of additional temporary objects.

    + 0

    Note that for large expressions this will be slower due to the allocation of additional temporary objects.

    diff --git a/previews/PR3913/manual/models/index.html b/previews/PR3913/manual/models/index.html index 5937d24adb2..5da671d8297 100644 --- a/previews/PR3913/manual/models/index.html +++ b/previews/PR3913/manual/models/index.html @@ -313,4 +313,4 @@ If you expected the solver to support your problem, you may have an error in your formulation. Otherwise, consider using a different solver. The list of available solvers, along with the problem types they support, is available at https://jump.dev/JuMP.jl/stable/installation/#Supported-solvers. -Stacktrace:
    Warning

    Another downside of direct mode is that the behavior of querying solution information after modifying the problem is solver-specific. This can lead to errors, or the solver silently returning an incorrect value. See OptimizeNotCalled errors for more information.

    +Stacktrace:
    Warning

    Another downside of direct mode is that the behavior of querying solution information after modifying the problem is solver-specific. This can lead to errors, or the solver silently returning an incorrect value. See OptimizeNotCalled errors for more information.

    diff --git a/previews/PR3913/manual/nlp/index.html b/previews/PR3913/manual/nlp/index.html index a31e25e7e73..4220a723328 100644 --- a/previews/PR3913/manual/nlp/index.html +++ b/previews/PR3913/manual/nlp/index.html @@ -344,4 +344,4 @@ f1(x[1]) - 1.0 ≤ 0 f2(x[1], x[2]) - 1.0 ≤ 0 f3(x[2], x[3], x[4]) - 1.0 ≤ 0 - f4(x[1], x[3], x[4], x[5]) - 1.0 ≤ 0

    Known performance issues

    The macro-based input to JuMP's nonlinear interface can cause a performance issue if you:

    1. write a macro with a large number (hundreds) of terms
    2. call that macro from within a function instead of from the top-level in global scope.

    The first issue does not depend on the number of resulting terms in the mathematical expression, but rather the number of terms in the Julia Expr representation of that expression. For example, the expression sum(x[i] for i in 1:1_000_000) contains one million mathematical terms, but the Expr representation is just a single sum.

    The most common cause, other than a lot of tedious typing, is if you write a program that automatically writes a JuMP model as a text file, which you later execute. One example is MINLPlib.jl which automatically transpiled models in the GAMS scalar format into JuMP examples.

    As a rule of thumb, if you are writing programs to automatically generate expressions for the JuMP macros, you should target the Raw expression input instead. For more information, read MathOptInterface Issue#1997.

    + f4(x[1], x[3], x[4], x[5]) - 1.0 ≤ 0

    Known performance issues

    The macro-based input to JuMP's nonlinear interface can cause a performance issue if you:

    1. write a macro with a large number (hundreds) of terms
    2. call that macro from within a function instead of from the top-level in global scope.

    The first issue does not depend on the number of resulting terms in the mathematical expression, but rather the number of terms in the Julia Expr representation of that expression. For example, the expression sum(x[i] for i in 1:1_000_000) contains one million mathematical terms, but the Expr representation is just a single sum.

    The most common cause, other than a lot of tedious typing, is if you write a program that automatically writes a JuMP model as a text file, which you later execute. One example is MINLPlib.jl which automatically transpiled models in the GAMS scalar format into JuMP examples.

    As a rule of thumb, if you are writing programs to automatically generate expressions for the JuMP macros, you should target the Raw expression input instead. For more information, read MathOptInterface Issue#1997.

    diff --git a/previews/PR3913/manual/nonlinear/index.html b/previews/PR3913/manual/nonlinear/index.html index f714aef15dc..6c85eff1c48 100644 --- a/previews/PR3913/manual/nonlinear/index.html +++ b/previews/PR3913/manual/nonlinear/index.html @@ -319,4 +319,4 @@ julia> ForwardDiff.gradient(x -> my_operator_good(x...), [1.0, 2.0]) 2-element Vector{Float64}: 2.0 - 4.0 + 4.0 diff --git a/previews/PR3913/manual/objective/index.html b/previews/PR3913/manual/objective/index.html index ef811bfc1c7..ca3d239c13f 100644 --- a/previews/PR3913/manual/objective/index.html +++ b/previews/PR3913/manual/objective/index.html @@ -179,4 +179,4 @@ 2 x[1] julia> @constraint(model, obj3 <= 2.0) -x[1] + x[2] ≤ 2 +x[1] + x[2] ≤ 2 diff --git a/previews/PR3913/manual/solutions/index.html b/previews/PR3913/manual/solutions/index.html index 60262d9a8c5..ddef5ffa882 100644 --- a/previews/PR3913/manual/solutions/index.html +++ b/previews/PR3913/manual/solutions/index.html @@ -430,4 +430,4 @@ x integer => 0.1

    You can also use the functional form, where the first argument is a function that maps variables to their primal values:

    julia> optimize!(model)
 
 julia> primal_feasibility_report(v -> value(v), model)
-Dict{Any, Float64}()
    +Dict{Any, Float64}() diff --git a/previews/PR3913/manual/variables/index.html b/previews/PR3913/manual/variables/index.html index f434204863d..6177b2ed68c 100644 --- a/previews/PR3913/manual/variables/index.html +++ b/previews/PR3913/manual/variables/index.html @@ -639,4 +639,4 @@ p*x julia> typeof(px) -QuadExpr (alias for GenericQuadExpr{Float64, GenericVariableRef{Float64}})

    When to use a parameter

    Parameters are most useful when solving nonlinear models in a sequence:

    julia> using JuMP, Ipopt
    julia> model = Model(Ipopt.Optimizer);
    julia> set_silent(model)
    julia> @variable(model, x)x
    julia> @variable(model, p in Parameter(1.0))p
    julia> @objective(model, Min, (x - p)^2)x² - 2 p*x + p²
    julia> optimize!(model)
    julia> value(x)1.0
    julia> set_parameter_value(p, 5.0)
    julia> optimize!(model)
    julia> value(x)5.0

    Using parameters can be faster than creating a new model from scratch with updated data because JuMP is able to avoid repeating a number of steps in processing the model before handing it off to the solver.

    +QuadExpr (alias for GenericQuadExpr{Float64, GenericVariableRef{Float64}})

    When to use a parameter

    Parameters are most useful when solving nonlinear models in a sequence:

    julia> using JuMP, Ipopt
    julia> model = Model(Ipopt.Optimizer);
    julia> set_silent(model)
    julia> @variable(model, x)x
    julia> @variable(model, p in Parameter(1.0))p
    julia> @objective(model, Min, (x - p)^2)x² - 2 p*x + p²
    julia> optimize!(model)
    julia> value(x)1.0
    julia> set_parameter_value(p, 5.0)
    julia> optimize!(model)
    julia> value(x)5.0

    Using parameters can be faster than creating a new model from scratch with updated data because JuMP is able to avoid repeating a number of steps in processing the model before handing it off to the solver.

    diff --git a/previews/PR3913/moi/background/duality/index.html b/previews/PR3913/moi/background/duality/index.html index ddc8a524cc2..299ea05cd1e 100644 --- a/previews/PR3913/moi/background/duality/index.html +++ b/previews/PR3913/moi/background/duality/index.html @@ -81,4 +81,4 @@ \max & \sum b_k y_k \\ \text{s.t.} \;\; & C+C^\top - \sum (A_k+A_k^\top) y_k \in \mathcal{S}_+ \\ & C-C^\top - \sum(A_k-A_k^\top) y_k = 0 -\end{align}\]

    and we recover $Z = X + X^\top$.

    +\end{align}\]

    and we recover $Z = X + X^\top$.

    diff --git a/previews/PR3913/moi/background/infeasibility_certificates/index.html b/previews/PR3913/moi/background/infeasibility_certificates/index.html index 593a373c112..88020f4a547 100644 --- a/previews/PR3913/moi/background/infeasibility_certificates/index.html +++ b/previews/PR3913/moi/background/infeasibility_certificates/index.html @@ -29,4 +29,4 @@ \end{align}\]

    and:

    \[-\sum_{i=1}^m b_i^\top (y_i + \eta d_i) > -\sum_{i=1}^m b_i^\top y_i,\]

    for any feasible dual solution $y$. The latter simplifies to $-\sum_{i=1}^m b_i^\top d_i > 0$. For a maximization problem, the inequality is $\sum_{i=1}^m b_i^\top d_i < 0$. (Note that these are the same inequality, modulo a - sign.)

    If the solver has found a certificate of primal infeasibility:

    Note

    The choice of whether to scale the ray $d$ to have magnitude 1 is left to the solver.

    Infeasibility certificates of variable bounds

    Many linear solvers (for example, Gurobi) do not provide explicit access to the primal infeasibility certificate of a variable bound. However, given a set of linear constraints:

    \[\begin{align} l_A \le A x \le u_A \\ l_x \le x \le u_x, -\end{align}\]

    the primal certificate of the variable bounds can be computed using the primal certificate associated with the affine constraints, $d$. (Note that $d$ will have one element for each row of the $A$ matrix, and that some or all of the elements in the vectors $l_A$ and $u_A$ may be $\pm \infty$. If both $l_A$ and $u_A$ are finite for some row, the corresponding element in `d must be 0.)

    Given $d$, compute $\bar{d} = d^\top A$. If the bound is finite, a certificate for the lower variable bound of $x_i$ is $\max\{\bar{d}_i, 0\}$, and a certificate for the upper variable bound is $\min\{\bar{d}_i, 0\}$.

    +\end{align}\]

    the primal certificate of the variable bounds can be computed using the primal certificate associated with the affine constraints, $d$. (Note that $d$ will have one element for each row of the $A$ matrix, and that some or all of the elements in the vectors $l_A$ and $u_A$ may be $\pm \infty$. If both $l_A$ and $u_A$ are finite for some row, the corresponding element in `d must be 0.)

    Given $d$, compute $\bar{d} = d^\top A$. If the bound is finite, a certificate for the lower variable bound of $x_i$ is $\max\{\bar{d}_i, 0\}$, and a certificate for the upper variable bound is $\min\{\bar{d}_i, 0\}$.

    diff --git a/previews/PR3913/moi/background/motivation/index.html b/previews/PR3913/moi/background/motivation/index.html index 01b6fcb260b..8842114004b 100644 --- a/previews/PR3913/moi/background/motivation/index.html +++ b/previews/PR3913/moi/background/motivation/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Motivation

    MathOptInterface (MOI) is a replacement for MathProgBase, the first-generation abstraction layer for mathematical optimization previously used by JuMP and Convex.jl.

    To address a number of limitations of MathProgBase, MOI is designed to:

    • Be simple and extensible
      • unifying linear, quadratic, and conic optimization,
      • seamlessly facilitating extensions to essentially arbitrary constraints and functions (for example, indicator constraints, complementarity constraints, and piecewise-linear functions)
    • Be fast
      • by allowing access to a solver's in-memory representation of a problem without writing intermediate files (when possible)
      • by using multiple dispatch and avoiding requiring containers of non-concrete types
    • Allow a solver to return multiple results (for example, a pool of solutions)
    • Allow a solver to return extra arbitrary information via attributes (for example, variable- and constraint-wise membership in an irreducible inconsistent subset for infeasibility analysis)
    • Provide a greatly expanded set of status codes explaining what happened during the optimization procedure
    • Enable a solver to more precisely specify which problem classes it supports
    • Enable both primal and dual warm starts
    • Enable adding and removing both variables and constraints by indices that are not required to be consecutive
    • Enable any modification that the solver supports to an existing model
    • Avoid requiring the solver wrapper to store an additional copy of the problem data
    +
    GitHub

    Motivation

    MathOptInterface (MOI) is a replacement for MathProgBase, the first-generation abstraction layer for mathematical optimization previously used by JuMP and Convex.jl.

    To address a number of limitations of MathProgBase, MOI is designed to:

    • Be simple and extensible
      • unifying linear, quadratic, and conic optimization,
      • seamlessly facilitating extensions to essentially arbitrary constraints and functions (for example, indicator constraints, complementarity constraints, and piecewise-linear functions)
    • Be fast
      • by allowing access to a solver's in-memory representation of a problem without writing intermediate files (when possible)
      • by using multiple dispatch and avoiding requiring containers of non-concrete types
    • Allow a solver to return multiple results (for example, a pool of solutions)
    • Allow a solver to return extra arbitrary information via attributes (for example, variable- and constraint-wise membership in an irreducible inconsistent subset for infeasibility analysis)
    • Provide a greatly expanded set of status codes explaining what happened during the optimization procedure
    • Enable a solver to more precisely specify which problem classes it supports
    • Enable both primal and dual warm starts
    • Enable adding and removing both variables and constraints by indices that are not required to be consecutive
    • Enable any modification that the solver supports to an existing model
    • Avoid requiring the solver wrapper to store an additional copy of the problem data
    diff --git a/previews/PR3913/moi/background/naming_conventions/index.html b/previews/PR3913/moi/background/naming_conventions/index.html index 0c42c419ada..4fff28cfcbe 100644 --- a/previews/PR3913/moi/background/naming_conventions/index.html +++ b/previews/PR3913/moi/background/naming_conventions/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Naming conventions

    MOI follows several conventions for naming functions and structures. These should also be followed by packages extending MOI.

    Sets

    Sets encode the structure of constraints. Their names should follow the following conventions:

    • Abstract types in the set hierarchy should begin with Abstract and end in Set, for example, AbstractScalarSet, AbstractVectorSet.
    • Vector-valued conic sets should end with Cone, for example, NormInfinityCone, SecondOrderCone.
    • Vector-valued Cartesian products should be plural and not end in Cone, for example, Nonnegatives, not NonnegativeCone.
    • Matrix-valued conic sets should provide two representations: ConeSquare and ConeTriangle, for example, RootDetConeTriangle and RootDetConeSquare. See Matrix cones for more details.
    • Scalar sets should be singular, not plural, for example, Integer, not Integers.
    • As much as possible, the names should follow established conventions in the domain where this set is used: for instance, convex sets should have names close to those of CVX, and constraint-programming sets should follow MiniZinc's constraints.
    +
    GitHub

    Naming conventions

    MOI follows several conventions for naming functions and structures. These should also be followed by packages extending MOI.

    Sets

    Sets encode the structure of constraints. Their names should follow the following conventions:

    • Abstract types in the set hierarchy should begin with Abstract and end in Set, for example, AbstractScalarSet, AbstractVectorSet.
    • Vector-valued conic sets should end with Cone, for example, NormInfinityCone, SecondOrderCone.
    • Vector-valued Cartesian products should be plural and not end in Cone, for example, Nonnegatives, not NonnegativeCone.
    • Matrix-valued conic sets should provide two representations: ConeSquare and ConeTriangle, for example, RootDetConeTriangle and RootDetConeSquare. See Matrix cones for more details.
    • Scalar sets should be singular, not plural, for example, Integer, not Integers.
    • As much as possible, the names should follow established conventions in the domain where this set is used: for instance, convex sets should have names close to those of CVX, and constraint-programming sets should follow MiniZinc's constraints.
    diff --git a/previews/PR3913/moi/changelog/index.html b/previews/PR3913/moi/changelog/index.html index 0e4f855c00b..20ac8b5c3b9 100644 --- a/previews/PR3913/moi/changelog/index.html +++ b/previews/PR3913/moi/changelog/index.html @@ -31,4 +31,4 @@ end write(path, s) end -end

    v0.9.22 (May 22, 2021)

    This release contains backports from the ongoing development of the v0.10 release.

    • Improved type inference in Utilities, Bridges and FileFormats submodules to reduce latency.
    • Improved performance of Utilities.is_canonical.
    • Fixed Utilities.pass_nonvariable_constraints with bridged variables.
    • Fixed performance regression of Utilities.Model.
    • Fixed ordering of objective setting in parser.

    v0.9.21 (April 23, 2021)

    • Added supports_shift_constant.
    • Improve performance of bridging quadratic constraints.
    • Add precompilation statements.
    • Large improvements to the documentation.
    • Fix a variety of inference issues, benefiting precompilation and reducing initial latency.
    • RawParameters are now ignored when resetting a CachingOptimizer. Previously, changing the underlying optimizer after RawParameters were set would throw an error.
    • Utilities.AbstractModel is being refactored. This may break users interacting with private fields of a model generated using @model.

    v0.9.20 (February 20, 2021)

    • Improved performance of Utilities.ScalarFunctionIterator
    • Added support for compute_conflict to MOI layers
    • Added test with zero off-diagonal quadratic term in objective
    • Fixed double deletion of nested bridged SingleVariable/VectorOfVariables constraints
    • Fixed modification of un-set objective
    • Fixed function modification with duplicate terms
    • Made unit tests abort without failing if the problem class is not supported
    • Formatted code with JuliaFormatter
    • Clarified BasisStatusCode's docstring

    v0.9.19 (December 1, 2020)

    • Added CallbackNodeStatus attribute
    • Added bridge from GreaterThan or LessThan to Interval
    • Added tests for infeasibility certificates and double optimize
    • Fixed support for Julia v1.6
    • Re-organized MOI docs and added documentation for adding a test

    v0.9.18 (November 3, 2020)

    • Various improvements for working with complex numbers
    • Added GeoMeantoRelEntrBridge to bridge a GeometricMeanCone constraint to a relative entropy constraint

    v0.9.17 (September 21, 2020)

    • Fixed CleverDict with variable of negative index value
    • Implement supports_add_constrained_variable for MockOptimizer

    v0.9.16 (September 17, 2020)

    • Various fixes:
      • 32-bit support
      • CleverDict with abstract value type
      • Checks in test suite

    v0.9.15 (September 14, 2020)

    • Bridges improvements:
      • (R)SOCtoNonConvexQuad bridge
      • ZeroOne bridge
      • Use supports_add_constrained_variable in LazyBridgeOptimizer
      • Exposed VariableBridgeCost and ConstraintBridgeCost attributes
      • Prioritize constraining variables on creation according to these costs
      • Refactor bridge debugging
    • Large performance improvements across all submodules
    • Lots of documentation improvements
    • FileFormats improvements:
      • Update MathOptFormat to v0.5
      • Fix supported objectives in FileFormats
    • Testing improvements:
      • Add name option for basic_constraint_test
    • Bug fixes and missing methods
      • Add length for iterators
      • Fix bug with duplicate terms
      • Fix order of LinearOfConstraintIndices

    v0.9.14 (May 30, 2020)

    • Add a solver-independent interface for accessing the set of conflicting constraints an Irreducible Inconsistent Subsystem (#1056).
    • Bump JSONSchema dependency from v0.2 to v0.3 (#1090).
    • Documentation improvements:
      • Fix typos (#1054, #1060, #1061, #1064, #1069, #1070).
      • Remove the outdated recommendation for a package implementing MOI for a solver XXX to be called MathOptInterfaceXXX (#1087).
    • Utilities improvements:
      • Fix is_canonical for quadratic functions (#1081, #1089).
      • Implement add_constrained_variable[s] for CachingOptimizer so that it is added as constrained variables to the underlying optimizer (#1084).
      • Add support for custom objective functions for UniversalFallback (#1086).
      • Deterministic ordering of constraints in UniversalFallback (#1088).
    • Testing improvements:
      • Add NormOneCone/NormInfinityCone tests (#1045).
    • Bridges improvements:
      • Add bridges from Semiinteger and Semicontinuous (#1059).
      • Implement getting ConstraintSet for Variable.FlipSignBridge (#1066).
      • Fix setting ConstraintFunction for Constraint.ScalarizeBridge (#1093).
      • Fix NormOne/NormInf bridges with nonzero constants (#1045).
      • Fix StackOverflow in debug (#1063).
    • FileFormats improvements:
      • [SDPA] Implement the extension for integer variables (#1079).
      • [SDPA] Ignore comments after m and nblocks and detect dat-s extension (#1077).
      • [SDPA] No scaling of off-diagonal coefficient (#1076).
      • [SDPA] Add missing negation of constant (#1075).

    v0.9.13 (March 24, 2020)

    • Added tests for Semicontinuous and Semiinteger variables (#1033).
    • Added tests for using ExprGraphs from NLP evaluators (#1043).
    • Update version compatibilities of dependencies (#1034, #1051, #1052).
    • Fixed typos in documentation (#1044).

    v0.9.12 (February 28, 2020)

    • Fixed writing NLPBlock in MathOptFormat (#1037).
    • Fixed MockOptimizer for result attributes with non-one result index (#1039).
    • Updated test template with instantiate (#1032).

    v0.9.11 (February 21, 2020)

    • Add an option for the model created by Utilities.@model to be a subtype of AbstractOptimizer (#1031).
    • Described dual cone in docstrings of GeoMeanCone and RelativeEntropyCone (#1018, #1028).
    • Fixed typos in documentation (#1022, #1024).
    • Fixed warning of unsupported attribute (#1027).
    • Added more rootdet/logdet conic tests (#1026).
    • Implemented ConstraintDual for Constraint.GeoMeanBridge, Constraint.RootDetBridge and Constraint.LogDetBridge and test duals in tests with GeoMeanCone and RootDetConeTriangle and LogDetConeTriangle cones (#1025, #1026).

    v0.9.10 (January 31, 2020)

    • Added OptimizerWithAttributes grouping an optimizer constructor and a list of optimizer attributes (#1008).
    • Added RelativeEntropyCone with corresponding bridge into exponential cone constraints (#993).
    • Added NormSpectralCone and NormNuclearCone with corresponding bridges into positive semidefinite constraints (#976).
    • Added supports_constrained_variable(s) (#1004).
    • Added dual_set_type (#1002).
    • Added tests for vector specialized version of delete (#989, #1011).
    • Added PSD3 test (#1007).
    • Clarified dual solution of Tests.pow1v and Tests.pow1f (#1013).
    • Added support for EqualTo and Zero in Bridges.Constraint.SplitIntervalBridge (#1005).
    • Fixed Utilities.vectorize for empty vector (#1003).
    • Fixed free variables in LP writer (#1006).

    v0.9.9 (December 29, 2019)

    • Incorporated MathOptFormat.jl as the FileFormats submodule. FileFormats provides readers and writers for a number of standard file formats and MOF, a file format specialized for MOI (#969).
    • Improved performance of deletion of vector of variables in MOI.Utilities.Model (#983).
    • Updated to MutableArithmetics v0.2 (#981).
    • Added MutableArithmetics.promote_operation allocation tests (#975).
    • Fixed inference issue on Julia v1.1 (#982).

    v0.9.8 (December 19, 2019)

    • Implemented MutableArithmetics API (#924).
    • Fixed callbacks with CachingOptimizer (#959).
    • Fixed MOI.dimension for MOI.Complements (#948).
    • Added fallback for add_variables (#972).
    • Added is_diagonal_vectorized_index utility (#965).
    • Improved linear constraints display in manual (#963, #964).
    • Bridges improvements:
      • Added IndicatorSet to SOS1 bridge (#877).
      • Added support for starting values for Variable.VectorizeBridge (#944).
      • Fixed MOI.add_constraints with non-bridged variable constraint on bridged variable (#951).
      • Fixed corner cases and docstring of GeoMeanBridge (#961, #962, #966).
      • Fixed choice between variable or constraint bridges for constrained variables (#973).
      • Improve performance of bridge shortest path (#945, #946, #956).
      • Added docstring for test_delete_bridge (#954).
      • Added Variable bridge tests (#952).

    v0.9.7 (October 30, 2019)

    • Implemented _result_index_field for NLPBlockDual (#934).
    • Fixed copy of model with starting values for vector constraints (#941).
    • Bridges improvements:
      • Improved performance of add_bridge and added has_bridge (#935).
      • Added AbstractSetMapBridge for bridges between sets S1, S2 such that there is a linear map A such that A*S1 = S2 (#933).
      • Added support for starting values for FlipSignBridge, VectorizeBridge, ScalarizeBridge, SlackBridge, SplitIntervalBridge, RSOCBridge, SOCRBridge NormInfinityBridge, SOCtoPSDBridge and RSOCtoPSDBridge (#933, #936, #937, #938, #939).

    v0.9.6 (October 25, 2019)

    • Added complementarity constraints (#913).
    • Allowed ModelLike objects as value of attributes (#928).
    • Testing improvements:
      • Added dual_objective_value option to MOI.Test.TestConfig (#922).
      • Added InvalidIndex tests in basic_constraint_tests (#921).
      • Added tests for the constant term in indicator constraint (#929).
    • Bridges improvements:
      • Added support for starting values for Functionize bridges (#923).
      • Added variable indices context to variable bridges (#920).
      • Fixed a typo in printing o debug_supports (#927).

    v0.9.5 (October 9, 2019)

    • Clarified PrimalStatus/DualStatus to be NO_SOLUTION if result_index is out of bounds (#912).
    • Added tolerance for checks and use ResultCount + 1 for the result_index in MOI.Test.solve_result_status (#910, #917).
    • Use 0.5 instead of 2.0 for power in PowerCone in basic_constraint_test (#916).
    • Bridges improvements:
      • Added debug utilities for unsupported variable/constraint/objective (#861).
      • Fixed deletion of variables in bridged VectorOfVariables constraints (#909).
      • Fixed result_index with objective bridges (#911).

    v0.9.4 (October 2, 2019)

    • Added solver-independent MIP callbacks (#782).
    • Implements submit for Utilities.CachingOptimizer and Bridges.AbstractBridgeOptimizer (#906).
    • Added tests for result count of solution attributes (#901, #904).
    • Added NumberOfThreads attribute (#892).
    • Added Utilities.get_bounds to get the bounds on a variable (#890).
    • Added a note on duplicate coefficients in documentation (#581).
    • Added result index in ConstraintBasisStatus (#898).
    • Added extension dictionary to Utilities.Model (#884, #895).
    • Fixed deletion of constrained variables for CachingOptimizer (#905).
    • Implemented Utilities.shift_constraint for Test.UnknownScalarSet (#896).
    • Bridges improvements:
      • Added Variable.RSOCtoSOCBridge (#907).
      • Implemented MOI.get for ConstraintFunction/ConstraintSet for Bridges.Constraint.SquareBridge (#899).

    v0.9.3 (September 20, 2019)

    • Fixed ambiguity detected in Julia v1.3 (#891, #893).
    • Fixed missing sets from ListOfSupportedConstraints (#880).
    • Fixed copy of VectorOfVariables constraints with duplicate indices (#886).
    • Added extension dictionary to MOIU.Model (#884).
    • Implemented MOI.get for function and set for GeoMeanBridge (#888).
    • Updated documentation for SingleVariable indices and bridges (#885).
    • Testing improvements:
      • Added more comprehensive tests for names (#882).
      • Added tests for SingleVariable duals (#883).
      • Added tests for DualExponentialCone and DualPowerCone (#873).
    • Improvements for arbitrary coefficient type:
      • Fixed == for sets with mutable fields (#887).
      • Removed some Float64 assumptions in bridges (#878).
      • Automatic selection of Constraint.[Scalar|Vector]FunctionizeBridge (#889).

    v0.9.2 (September 5, 2019)

    • Implemented model printing for MOI.ModelLike and specialized it for models defined in MOI (864).
    • Generalized contlinear tests for arbitrary coefficient type (#855).
    • Fixed supports_constraint for Semiinteger and Semicontinuous and supports for ObjectiveFunction (#859).
    • Fixed Allocate-Load copy for single variable constraints (#856).
    • Bridges improvements:
      • Add objective bridges (#789).
      • Fixed Variable.RSOCtoPSDBridge for dimension 2 (#869).
      • Added Variable.SOCtoRSOCBridge (#865).
      • Added Constraint.SOCRBridge and disable MOI.Bridges.Constraint.SOCtoPSDBridge (#751).
      • Fixed added_constraint_types for Contraint.LogDetBridge and Constraint.RootDetBridge (#870).

    v0.9.1 (August 22, 2019)

    • Fix support for Julia v1.2 (#834).
    • L1 and L∞ norm epigraph cones and corresponding bridges to LP were added (#818).
    • Added tests to MOI.Test.nametest (#833).
    • Fix MOI.Test.soc3test for solvers not supporting infeasibility certificates (#839).
    • Implements operate for operators * and / between vector function and constant (#837).
    • Implements show for MOI.Utilities.IndexMap (#847).
    • Fix corner cases for mapping of variables in MOI.Utilities.CachingOptimizer and substitution of variables in MOI.Bridges.AbstractBridgeOptimizer (#848).
    • Fix transformation of constant terms for MOI.Bridges.Constraint.SOCtoPSDBridge and MOI.Bridges.Constraint.RSOCtoPSDBridge (#840).

    v0.9.0 (August 13, 2019)

    • Support for Julia v0.6 and v0.7 was dropped (#714, #717).
    • A MOI.Utilities.Model implementation of ModelLike, this should replace most use cases of MOI.Utilities.@model (#781).
    • add_constrained_variable and add_constrained_variables were added (#759).
    • Support for indicator constraints was added (#709, #712).
    • DualObjectiveValue attribute was added (#473).
    • RawParameter attribute was added (#733).
    • A dual_set function was added (#804).
    • A Benchmarks submodule was added to facilitate solver benchmarking (#769).
    • A submit function was added, this may for instance allow the user to submit solutions or cuts to the solver from a callback (#775).
    • The field of ObjectiveValue was renamed to result_index (#729).
    • The _constant and Utilities.getconstant function were renamed to constant
    • REDUCTION_CERTIFICATE result status was added (#734).
    • Abstract matrix sets were added (#731).
    • Testing improvements:
      • The testing guideline was updated (#728).
      • Quadratic tests were added (#697).
      • Unit tests for RawStatusString, SolveTime, Silent and SolverName were added (#726, #741).
      • A rotated second-order cone test was added (#759).
      • A power cone test was added (#768).
      • Tests for ZeroOne variables with variable bounds were added (#772).
      • An unbounded test was added (#773).
      • Existing tests had a few updates (#702, #703, #763).
    • Documentation improvements:
      • Added a section on CachingOptimizer (#777).
      • Added a section on UniversalFallback, Model and @model (#762).
      • Transition the knapsack example to a doctest with MockOptimizer (#786).
    • Utilities improvements:
      • A CleverDict utility was added for a vector that automatically transform into a dictionary once a first index is removed (#767).
      • The Utilities.constant function was renamed to Utilities.constant_vector (#740).
      • Implement optimizer attributes for CachingOptimizer (#745).
      • Rename Utilities.add_scalar_constraint to Utilities.normalize_and_add_constraint (#801).
      • operate with vcat, SingleVariable and VectorOfVariables now returns a VectorOfVariables (#616).
      • Fix a type piracy of operate (#784).
      • The load_constraint fallback signature was fixed (#760).
      • The set_dot function was extended to work with sparse arrays (#805).
    • Bridges improvements:
      • The bridges no longer store the constraint function and set before it is bridged, the bridges now have to implement ConstraintFunction and ConstraintSet if the user wants to recover them. As a consequence, the @bridge macro was removed (#722).
      • Bridge are now instantiated with a bridge_constraint function instead of using a constructor (#730).
      • Fix constraint attributes for bridges (#699).
      • Constraint bridges were moved to the Bridges/Constraint submodule so they should now inherit from MOI.Bridges.Constraint.Abstract and should implement MOI.Bridges.Constraint.concrete_bridge_type instead of MOI.Bridges.concrete_bridge_type (#756).
      • Variable bridges were added in (#759).
      • Various improvements (#746, #747).

    v0.8.4 (March 13, 2019)

    • Performance improvement in default_copy_to and bridge optimizer (#696).
    • Add Silent and implement setting optimizer attributes in caching and mock optimizers (#695).
    • Add Functionize bridges (SingleVariable and VectorOfVariables) (#659).
    • Minor typo fixes (#694).

    v0.8.3 (March 6, 2019)

    • Use zero constant in scalar constraint function of MOI.Test.copytest (#691).
    • Fix variable deletion with SingleVariable objective function (#690).
    • Fix LazyBridgeOptimizer with bridges that add no constraints (#689).
    • Error message improvements (#673, #685, #686, #688).
    • Documentation improvements (#682, #683, #687).
    • Basis status:
      • Remove VariableBasisStatus (#679).
      • Test ConstraintBasisStatus and implement it in bridges (#678).
    • Fix inference of NumberOfVariables and NumberOfConstraints (#677).
    • Implement division between a quadratic function and a number (#675).

    v0.8.2 (February 7, 2019)

    • Add RawStatusString attribute (#629).
    • Do not set names to the optimizer but only to the cache in CachingOptimizer (#638).
    • Make scalar MOI functions act as scalars in broadcast (#646).
    • Add function utilities:
      • Implement Base.zero (#634), Base.iszero (#643), add missing arithmetic operations (#644, #645) and fix division (#648).
      • Add a vectorize function that turns a vector of ScalarAffineFunction into a VectorAffineFunction (#642).
    • Improve support for starting values:
      • Show a warning in copy when starting values are not supported instead of throwing an error (#630).
      • Fix UniversalFallback for getting an variable or constraint attribute set to no indices (#623).
      • Add a test in contlineartest with partially set VariablePrimalStart.
    • Bridges improvements:
      • Fix StackOverFlow in LazyBridgeOptimizer when there is a cycle in the graph of bridges.
      • Add Slack bridges (#610, #650).
      • Add FlipSign bridges (#658).
    • Add tests with duplicate coefficients in ScalarAffineFunction and VectorAffineFunction (#639).
    • Use tolerance to compare VariablePrimal in rotatedsoc1 test (#632).
    • Use a zero constant in ScalarAffineFunction of constraints in psdt2 (#622).

    v0.8.1 (January 7, 2019)

    • Adding an NLP objective now overrides any objective set using the ObjectiveFunction attribute (#619).
    • Rename fullbridgeoptimizer into full_bridge_optimizer (#621).
    • Allow custom constraint types with full_bridge_optimizer (#617).
    • Add Vectorize bridge which transforms scalar linear constraints into vector linear constraints (#615).

    v0.8.0 (December 18, 2018)

    • Rename all enum values to follow the JuMP naming guidelines for constants, for example, Optimal becomes OPTIMAL, and DualInfeasible becomes DUAL_INFEASIBLE.
    • Rename CachingOptimizer methods for style compliance.
    • Add an MOI.TerminationStatusCode called ALMOST_DUAL_INFEASIBLE.

    v0.7.0 (December 13, 2018)

    • Test that MOI.TerminationStatus is MOI.OptimizeNotCalled before MOI.optimize! is called.
    • Check supports_default_copy_to in tests (#594).
    • Key pieces of information like optimality, infeasibility, etc., are now reported through TerminationStatusCode. It is typically no longer necessary to check the result statuses in addition to the termination status.
    • Add perspective dimension to log-det cone (#593).

    v0.6.4 (November 27, 2018)

    • Add OptimizeNotCalled termination status (#577) and improve documentation of other statuses (#575).
    • Add a solver naming guideline (#578).
    • Make FeasibilitySense the default ObjectiveSense (#579).
    • Fix Utilities.@model and Bridges.@bridge macros for functions and sets defined outside MOI (#582).
    • Document solver-specific attributes (#580) and implement them in Utilities.CachingOptimizer (#565).

    v0.6.3 (November 16, 2018)

    • Variables and constraints are now allowed to have duplicate names. An error is thrown only on lookup. This change breaks some existing tests. (#549)
    • Attributes may now be partially set (some values could be nothing). (#563)
    • Performance improvements in Utilities.Model (#549, #567, #568)
    • Fix bug in QuadtoSOC (#558).
    • New supports_default_copy_to method that optimizers should implement to control caching behavior.
    • Documentation improvements.

    v0.6.2 (October 26, 2018)

    • Improve hygiene of @model macro (#544).
    • Fix bug in copy tests (#543).
    • Fix bug in UniversalFallback attribute getter (#540).
    • Allow all correct solutions for solve_blank_obj unit test (#537).
    • Add errors for Allocate-Load and bad constraints (#534).
    • [performance] Add specialized implementation of hash for VariableIndex (#533).
    • [performance] Construct the name to object dictionaries lazily in model (#535).
    • Add the QuadtoSOC bridge which transforms ScalarQuadraticFunction constraints into RotatedSecondOrderCone (#483).

    v0.6.1 (September 22, 2018)

    • Enable PositiveSemidefiniteConeSquare set and quadratic functions in MOIB.fullbridgeoptimizer (#524).
    • Add warning in the bridge between PositiveSemidefiniteConeSquare and PositiveSemidefiniteConeTriangle when the matrix is almost symmetric (#522).
    • Modify MOIT.copytest to not add multiples constraints on the same variable (#521).
    • Add missing keyword argument in one of MOIU.add_scalar_constraint methods (#520).

    v0.6.0 (August 30, 2018)

    • The MOIU.@model and MOIB.@bridge macros now support functions and sets defined in external modules. As a consequence, function and set names in the macro arguments need to be prefixed by module name.
    • Rename functions according to the JuMP style guide:
      • copy! with keyword arguments copynames and warnattributes -> copy_to with keyword arguments copy_names and warn_attributes;
      • set! -> set;
      • addvariable[s]! -> add_variable[s];
      • supportsconstraint -> supports_constraint;
      • addconstraint[s]! -> add_constraint[s];
      • isvalid -> is_valid;
      • isempty -> is_empty;
      • Base.delete! -> delete;
      • modify! -> modify;
      • transform! -> transform;
      • initialize! -> initialize;
      • write -> write_to_file; and
      • read! -> read_from_file.
    • Remove free! (use Base.finalize instead).
    • Add the SquarePSD bridge which transforms PositiveSemidefiniteConeTriangle constraints into PositiveSemidefiniteConeTriangle.
    • Add result fallback for ConstraintDual of variable-wise constraint, ConstraintPrimal and ObjectiveValue.
    • Add tests for ObjectiveBound.
    • Add test for empty rows in vector linear constraint.
    • Rework errors: CannotError has been renamed NotAllowedError and the distinction between UnsupportedError and NotAllowedError is now about whether the element is not supported (for example, it cannot be copied a model containing this element) or the operation is not allowed (either because it is not implemented, because it cannot be performed in the current state of the model, or because it cannot be performed for a specific index)
    • canget is removed. NoSolution is added as a result status to indicate that the solver does not have either a primal or dual solution available (See #479).

    v0.5.0 (August 5, 2018)

    • Fix names with CachingOptimizer.
    • Cleanup thanks to @mohamed82008.
    • Added a universal fallback for constraints.
    • Fast utilities for function canonicalization thanks to @rdeits.
    • Renamed dimension field to side_dimension in the context of matrix-like sets.
    • New and improved tests for cases like duplicate terms and ObjectiveBound.
    • Removed cantransform, canaddconstraint, canaddvariable, canset, canmodify, and candelete functions from the API. They are replaced by a new set of errors that are thrown: Subtypes of UnsupportedError indicate unsupported operations, while subtypes of CannotError indicate operations that cannot be performed in the current state.
    • The API for copy! is updated to remove the CopyResult type.
    • Updates for the new JuMP style guide.

    v0.4.1 (June 28, 2018)

    • Fixes vector function modification on 32 bits.
    • Fixes Bellman-Ford algorithm for bridges.
    • Added an NLP test with FeasibilitySense.
    • Update modification documentation.

    v0.4.0 (June 23, 2018)

    • Helper constructors for VectorAffineTerm and VectorQuadraticTerm.
    • Added modify_lhs to TestConfig.
    • Additional unit tests for optimizers.
    • Added a type parameter to CachingOptimizer for the optimizer field.
    • New API for problem modification (#388)
    • Tests pass without deprecation warnings on Julia 0.7.
    • Small fixes and documentation updates.

    v0.3.0 (May 25, 2018)

    • Functions have been redefined to use arrays-of-structs instead of structs-of-arrays.
    • Improvements to MockOptimizer.
    • Significant changes to Bridges.
    • New and improved unit tests.
    • Fixes for Julia 0.7.

    v0.2.0 (April 24, 2018)

    • Improvements to and better coverage of Tests.
    • Documentation fixes.
    • SolverName attribute.
    • Changes to the NLP interface (new definition of variable order and arrays of structs for bound pairs and sparsity patterns).
    • Addition of NLP tests.
    • Introduction of UniversalFallback.
    • copynames keyword argument to MOI.copy!.
    • Add Bridges submodule.

    v0.1.0 (February 28, 2018)

    • Initial public release.
    • The framework for MOI was developed at the JuMP-dev workshop at MIT in June 2017 as a sorely needed replacement for MathProgBase.
    +end

    v0.9.22 (May 22, 2021)

    This release contains backports from the ongoing development of the v0.10 release.

    • Improved type inference in Utilities, Bridges and FileFormats submodules to reduce latency.
    • Improved performance of Utilities.is_canonical.
    • Fixed Utilities.pass_nonvariable_constraints with bridged variables.
    • Fixed performance regression of Utilities.Model.
    • Fixed ordering of objective setting in parser.

    v0.9.21 (April 23, 2021)

    • Added supports_shift_constant.
    • Improve performance of bridging quadratic constraints.
    • Add precompilation statements.
    • Large improvements to the documentation.
    • Fix a variety of inference issues, benefiting precompilation and reducing initial latency.
    • RawParameters are now ignored when resetting a CachingOptimizer. Previously, changing the underlying optimizer after RawParameters were set would throw an error.
    • Utilities.AbstractModel is being refactored. This may break users interacting with private fields of a model generated using @model.

    v0.9.20 (February 20, 2021)

    • Improved performance of Utilities.ScalarFunctionIterator
    • Added support for compute_conflict to MOI layers
    • Added test with zero off-diagonal quadratic term in objective
    • Fixed double deletion of nested bridged SingleVariable/VectorOfVariables constraints
    • Fixed modification of un-set objective
    • Fixed function modification with duplicate terms
    • Made unit tests abort without failing if the problem class is not supported
    • Formatted code with JuliaFormatter
    • Clarified BasisStatusCode's docstring

    v0.9.19 (December 1, 2020)

    • Added CallbackNodeStatus attribute
    • Added bridge from GreaterThan or LessThan to Interval
    • Added tests for infeasibility certificates and double optimize
    • Fixed support for Julia v1.6
    • Re-organized MOI docs and added documentation for adding a test

    v0.9.18 (November 3, 2020)

    • Various improvements for working with complex numbers
    • Added GeoMeantoRelEntrBridge to bridge a GeometricMeanCone constraint to a relative entropy constraint

    v0.9.17 (September 21, 2020)

    • Fixed CleverDict with variable of negative index value
    • Implement supports_add_constrained_variable for MockOptimizer

    v0.9.16 (September 17, 2020)

    • Various fixes:
      • 32-bit support
      • CleverDict with abstract value type
      • Checks in test suite

    v0.9.15 (September 14, 2020)

    • Bridges improvements:
      • (R)SOCtoNonConvexQuad bridge
      • ZeroOne bridge
      • Use supports_add_constrained_variable in LazyBridgeOptimizer
      • Exposed VariableBridgeCost and ConstraintBridgeCost attributes
      • Prioritize constraining variables on creation according to these costs
      • Refactor bridge debugging
    • Large performance improvements across all submodules
    • Lots of documentation improvements
    • FileFormats improvements:
      • Update MathOptFormat to v0.5
      • Fix supported objectives in FileFormats
    • Testing improvements:
      • Add name option for basic_constraint_test
    • Bug fixes and missing methods
      • Add length for iterators
      • Fix bug with duplicate terms
      • Fix order of LinearOfConstraintIndices

    v0.9.14 (May 30, 2020)

    • Add a solver-independent interface for accessing the set of conflicting constraints an Irreducible Inconsistent Subsystem (#1056).
    • Bump JSONSchema dependency from v0.2 to v0.3 (#1090).
    • Documentation improvements:
      • Fix typos (#1054, #1060, #1061, #1064, #1069, #1070).
      • Remove the outdated recommendation for a package implementing MOI for a solver XXX to be called MathOptInterfaceXXX (#1087).
    • Utilities improvements:
      • Fix is_canonical for quadratic functions (#1081, #1089).
      • Implement add_constrained_variable[s] for CachingOptimizer so that it is added as constrained variables to the underlying optimizer (#1084).
      • Add support for custom objective functions for UniversalFallback (#1086).
      • Deterministic ordering of constraints in UniversalFallback (#1088).
    • Testing improvements:
      • Add NormOneCone/NormInfinityCone tests (#1045).
    • Bridges improvements:
      • Add bridges from Semiinteger and Semicontinuous (#1059).
      • Implement getting ConstraintSet for Variable.FlipSignBridge (#1066).
      • Fix setting ConstraintFunction for Constraint.ScalarizeBridge (#1093).
      • Fix NormOne/NormInf bridges with nonzero constants (#1045).
      • Fix StackOverflow in debug (#1063).
    • FileFormats improvements:
      • [SDPA] Implement the extension for integer variables (#1079).
      • [SDPA] Ignore comments after m and nblocks and detect dat-s extension (#1077).
      • [SDPA] No scaling of off-diagonal coefficient (#1076).
      • [SDPA] Add missing negation of constant (#1075).

    v0.9.13 (March 24, 2020)

    • Added tests for Semicontinuous and Semiinteger variables (#1033).
    • Added tests for using ExprGraphs from NLP evaluators (#1043).
    • Update version compatibilities of dependencies (#1034, #1051, #1052).
    • Fixed typos in documentation (#1044).

    v0.9.12 (February 28, 2020)

    • Fixed writing NLPBlock in MathOptFormat (#1037).
    • Fixed MockOptimizer for result attributes with non-one result index (#1039).
    • Updated test template with instantiate (#1032).

    v0.9.11 (February 21, 2020)

    • Add an option for the model created by Utilities.@model to be a subtype of AbstractOptimizer (#1031).
    • Described dual cone in docstrings of GeoMeanCone and RelativeEntropyCone (#1018, #1028).
    • Fixed typos in documentation (#1022, #1024).
    • Fixed warning of unsupported attribute (#1027).
    • Added more rootdet/logdet conic tests (#1026).
    • Implemented ConstraintDual for Constraint.GeoMeanBridge, Constraint.RootDetBridge and Constraint.LogDetBridge and test duals in tests with GeoMeanCone and RootDetConeTriangle and LogDetConeTriangle cones (#1025, #1026).

    v0.9.10 (January 31, 2020)

    • Added OptimizerWithAttributes grouping an optimizer constructor and a list of optimizer attributes (#1008).
    • Added RelativeEntropyCone with corresponding bridge into exponential cone constraints (#993).
    • Added NormSpectralCone and NormNuclearCone with corresponding bridges into positive semidefinite constraints (#976).
    • Added supports_constrained_variable(s) (#1004).
    • Added dual_set_type (#1002).
    • Added tests for vector specialized version of delete (#989, #1011).
    • Added PSD3 test (#1007).
    • Clarified dual solution of Tests.pow1v and Tests.pow1f (#1013).
    • Added support for EqualTo and Zero in Bridges.Constraint.SplitIntervalBridge (#1005).
    • Fixed Utilities.vectorize for empty vector (#1003).
    • Fixed free variables in LP writer (#1006).

    v0.9.9 (December 29, 2019)

    • Incorporated MathOptFormat.jl as the FileFormats submodule. FileFormats provides readers and writers for a number of standard file formats and MOF, a file format specialized for MOI (#969).
    • Improved performance of deletion of vector of variables in MOI.Utilities.Model (#983).
    • Updated to MutableArithmetics v0.2 (#981).
    • Added MutableArithmetics.promote_operation allocation tests (#975).
    • Fixed inference issue on Julia v1.1 (#982).

    v0.9.8 (December 19, 2019)

    • Implemented MutableArithmetics API (#924).
    • Fixed callbacks with CachingOptimizer (#959).
    • Fixed MOI.dimension for MOI.Complements (#948).
    • Added fallback for add_variables (#972).
    • Added is_diagonal_vectorized_index utility (#965).
    • Improved linear constraints display in manual (#963, #964).
    • Bridges improvements:
      • Added IndicatorSet to SOS1 bridge (#877).
      • Added support for starting values for Variable.VectorizeBridge (#944).
      • Fixed MOI.add_constraints with non-bridged variable constraint on bridged variable (#951).
      • Fixed corner cases and docstring of GeoMeanBridge (#961, #962, #966).
      • Fixed choice between variable or constraint bridges for constrained variables (#973).
      • Improve performance of bridge shortest path (#945, #946, #956).
      • Added docstring for test_delete_bridge (#954).
      • Added Variable bridge tests (#952).

    v0.9.7 (October 30, 2019)

    • Implemented _result_index_field for NLPBlockDual (#934).
    • Fixed copy of model with starting values for vector constraints (#941).
    • Bridges improvements:
      • Improved performance of add_bridge and added has_bridge (#935).
      • Added AbstractSetMapBridge for bridges between sets S1, S2 such that there is a linear map A such that A*S1 = S2 (#933).
      • Added support for starting values for FlipSignBridge, VectorizeBridge, ScalarizeBridge, SlackBridge, SplitIntervalBridge, RSOCBridge, SOCRBridge NormInfinityBridge, SOCtoPSDBridge and RSOCtoPSDBridge (#933, #936, #937, #938, #939).

    v0.9.6 (October 25, 2019)

    • Added complementarity constraints (#913).
    • Allowed ModelLike objects as value of attributes (#928).
    • Testing improvements:
      • Added dual_objective_value option to MOI.Test.TestConfig (#922).
      • Added InvalidIndex tests in basic_constraint_tests (#921).
      • Added tests for the constant term in indicator constraint (#929).
    • Bridges improvements:
      • Added support for starting values for Functionize bridges (#923).
      • Added variable indices context to variable bridges (#920).
      • Fixed a typo in printing o debug_supports (#927).

    v0.9.5 (October 9, 2019)

    • Clarified PrimalStatus/DualStatus to be NO_SOLUTION if result_index is out of bounds (#912).
    • Added tolerance for checks and use ResultCount + 1 for the result_index in MOI.Test.solve_result_status (#910, #917).
    • Use 0.5 instead of 2.0 for power in PowerCone in basic_constraint_test (#916).
    • Bridges improvements:
      • Added debug utilities for unsupported variable/constraint/objective (#861).
      • Fixed deletion of variables in bridged VectorOfVariables constraints (#909).
      • Fixed result_index with objective bridges (#911).

    v0.9.4 (October 2, 2019)

    • Added solver-independent MIP callbacks (#782).
    • Implements submit for Utilities.CachingOptimizer and Bridges.AbstractBridgeOptimizer (#906).
    • Added tests for result count of solution attributes (#901, #904).
    • Added NumberOfThreads attribute (#892).
    • Added Utilities.get_bounds to get the bounds on a variable (#890).
    • Added a note on duplicate coefficients in documentation (#581).
    • Added result index in ConstraintBasisStatus (#898).
    • Added extension dictionary to Utilities.Model (#884, #895).
    • Fixed deletion of constrained variables for CachingOptimizer (#905).
    • Implemented Utilities.shift_constraint for Test.UnknownScalarSet (#896).
    • Bridges improvements:
      • Added Variable.RSOCtoSOCBridge (#907).
      • Implemented MOI.get for ConstraintFunction/ConstraintSet for Bridges.Constraint.SquareBridge (#899).

    v0.9.3 (September 20, 2019)

    • Fixed ambiguity detected in Julia v1.3 (#891, #893).
    • Fixed missing sets from ListOfSupportedConstraints (#880).
    • Fixed copy of VectorOfVariables constraints with duplicate indices (#886).
    • Added extension dictionary to MOIU.Model (#884).
    • Implemented MOI.get for function and set for GeoMeanBridge (#888).
    • Updated documentation for SingleVariable indices and bridges (#885).
    • Testing improvements:
      • Added more comprehensive tests for names (#882).
      • Added tests for SingleVariable duals (#883).
      • Added tests for DualExponentialCone and DualPowerCone (#873).
    • Improvements for arbitrary coefficient type:
      • Fixed == for sets with mutable fields (#887).
      • Removed some Float64 assumptions in bridges (#878).
      • Automatic selection of Constraint.[Scalar|Vector]FunctionizeBridge (#889).

    v0.9.2 (September 5, 2019)

    • Implemented model printing for MOI.ModelLike and specialized it for models defined in MOI (864).
    • Generalized contlinear tests for arbitrary coefficient type (#855).
    • Fixed supports_constraint for Semiinteger and Semicontinuous and supports for ObjectiveFunction (#859).
    • Fixed Allocate-Load copy for single variable constraints (#856).
    • Bridges improvements:
      • Add objective bridges (#789).
      • Fixed Variable.RSOCtoPSDBridge for dimension 2 (#869).
      • Added Variable.SOCtoRSOCBridge (#865).
      • Added Constraint.SOCRBridge and disable MOI.Bridges.Constraint.SOCtoPSDBridge (#751).
      • Fixed added_constraint_types for Contraint.LogDetBridge and Constraint.RootDetBridge (#870).

    v0.9.1 (August 22, 2019)

    • Fix support for Julia v1.2 (#834).
    • L1 and L∞ norm epigraph cones and corresponding bridges to LP were added (#818).
    • Added tests to MOI.Test.nametest (#833).
    • Fix MOI.Test.soc3test for solvers not supporting infeasibility certificates (#839).
    • Implements operate for operators * and / between vector function and constant (#837).
    • Implements show for MOI.Utilities.IndexMap (#847).
    • Fix corner cases for mapping of variables in MOI.Utilities.CachingOptimizer and substitution of variables in MOI.Bridges.AbstractBridgeOptimizer (#848).
    • Fix transformation of constant terms for MOI.Bridges.Constraint.SOCtoPSDBridge and MOI.Bridges.Constraint.RSOCtoPSDBridge (#840).

    v0.9.0 (August 13, 2019)

    • Support for Julia v0.6 and v0.7 was dropped (#714, #717).
    • A MOI.Utilities.Model implementation of ModelLike, this should replace most use cases of MOI.Utilities.@model (#781).
    • add_constrained_variable and add_constrained_variables were added (#759).
    • Support for indicator constraints was added (#709, #712).
    • DualObjectiveValue attribute was added (#473).
    • RawParameter attribute was added (#733).
    • A dual_set function was added (#804).
    • A Benchmarks submodule was added to facilitate solver benchmarking (#769).
    • A submit function was added, this may for instance allow the user to submit solutions or cuts to the solver from a callback (#775).
    • The field of ObjectiveValue was renamed to result_index (#729).
    • The _constant and Utilities.getconstant function were renamed to constant
    • REDUCTION_CERTIFICATE result status was added (#734).
    • Abstract matrix sets were added (#731).
    • Testing improvements:
      • The testing guideline was updated (#728).
      • Quadratic tests were added (#697).
      • Unit tests for RawStatusString, SolveTime, Silent and SolverName were added (#726, #741).
      • A rotated second-order cone test was added (#759).
      • A power cone test was added (#768).
      • Tests for ZeroOne variables with variable bounds were added (#772).
      • An unbounded test was added (#773).
      • Existing tests had a few updates (#702, #703, #763).
    • Documentation improvements:
      • Added a section on CachingOptimizer (#777).
      • Added a section on UniversalFallback, Model and @model (#762).
      • Transition the knapsack example to a doctest with MockOptimizer (#786).
    • Utilities improvements:
      • A CleverDict utility was added for a vector that automatically transform into a dictionary once a first index is removed (#767).
      • The Utilities.constant function was renamed to Utilities.constant_vector (#740).
      • Implement optimizer attributes for CachingOptimizer (#745).
      • Rename Utilities.add_scalar_constraint to Utilities.normalize_and_add_constraint (#801).
      • operate with vcat, SingleVariable and VectorOfVariables now returns a VectorOfVariables (#616).
      • Fix a type piracy of operate (#784).
      • The load_constraint fallback signature was fixed (#760).
      • The set_dot function was extended to work with sparse arrays (#805).
    • Bridges improvements:
      • The bridges no longer store the constraint function and set before it is bridged, the bridges now have to implement ConstraintFunction and ConstraintSet if the user wants to recover them. As a consequence, the @bridge macro was removed (#722).
      • Bridge are now instantiated with a bridge_constraint function instead of using a constructor (#730).
      • Fix constraint attributes for bridges (#699).
      • Constraint bridges were moved to the Bridges/Constraint submodule so they should now inherit from MOI.Bridges.Constraint.Abstract and should implement MOI.Bridges.Constraint.concrete_bridge_type instead of MOI.Bridges.concrete_bridge_type (#756).
      • Variable bridges were added in (#759).
      • Various improvements (#746, #747).

    v0.8.4 (March 13, 2019)

    • Performance improvement in default_copy_to and bridge optimizer (#696).
    • Add Silent and implement setting optimizer attributes in caching and mock optimizers (#695).
    • Add Functionize bridges (SingleVariable and VectorOfVariables) (#659).
    • Minor typo fixes (#694).

    v0.8.3 (March 6, 2019)

    • Use zero constant in scalar constraint function of MOI.Test.copytest (#691).
    • Fix variable deletion with SingleVariable objective function (#690).
    • Fix LazyBridgeOptimizer with bridges that add no constraints (#689).
    • Error message improvements (#673, #685, #686, #688).
    • Documentation improvements (#682, #683, #687).
    • Basis status:
      • Remove VariableBasisStatus (#679).
      • Test ConstraintBasisStatus and implement it in bridges (#678).
    • Fix inference of NumberOfVariables and NumberOfConstraints (#677).
    • Implement division between a quadratic function and a number (#675).

    v0.8.2 (February 7, 2019)

    • Add RawStatusString attribute (#629).
    • Do not set names to the optimizer but only to the cache in CachingOptimizer (#638).
    • Make scalar MOI functions act as scalars in broadcast (#646).
    • Add function utilities:
      • Implement Base.zero (#634), Base.iszero (#643), add missing arithmetic operations (#644, #645) and fix division (#648).
      • Add a vectorize function that turns a vector of ScalarAffineFunction into a VectorAffineFunction (#642).
    • Improve support for starting values:
      • Show a warning in copy when starting values are not supported instead of throwing an error (#630).
      • Fix UniversalFallback for getting an variable or constraint attribute set to no indices (#623).
      • Add a test in contlineartest with partially set VariablePrimalStart.
    • Bridges improvements:
      • Fix StackOverFlow in LazyBridgeOptimizer when there is a cycle in the graph of bridges.
      • Add Slack bridges (#610, #650).
      • Add FlipSign bridges (#658).
    • Add tests with duplicate coefficients in ScalarAffineFunction and VectorAffineFunction (#639).
    • Use tolerance to compare VariablePrimal in rotatedsoc1 test (#632).
    • Use a zero constant in ScalarAffineFunction of constraints in psdt2 (#622).

    v0.8.1 (January 7, 2019)

    • Adding an NLP objective now overrides any objective set using the ObjectiveFunction attribute (#619).
    • Rename fullbridgeoptimizer into full_bridge_optimizer (#621).
    • Allow custom constraint types with full_bridge_optimizer (#617).
    • Add Vectorize bridge which transforms scalar linear constraints into vector linear constraints (#615).

    v0.8.0 (December 18, 2018)

    • Rename all enum values to follow the JuMP naming guidelines for constants, for example, Optimal becomes OPTIMAL, and DualInfeasible becomes DUAL_INFEASIBLE.
    • Rename CachingOptimizer methods for style compliance.
    • Add an MOI.TerminationStatusCode called ALMOST_DUAL_INFEASIBLE.

    v0.7.0 (December 13, 2018)

    • Test that MOI.TerminationStatus is MOI.OptimizeNotCalled before MOI.optimize! is called.
    • Check supports_default_copy_to in tests (#594).
    • Key pieces of information like optimality, infeasibility, etc., are now reported through TerminationStatusCode. It is typically no longer necessary to check the result statuses in addition to the termination status.
    • Add perspective dimension to log-det cone (#593).

    v0.6.4 (November 27, 2018)

    • Add OptimizeNotCalled termination status (#577) and improve documentation of other statuses (#575).
    • Add a solver naming guideline (#578).
    • Make FeasibilitySense the default ObjectiveSense (#579).
    • Fix Utilities.@model and Bridges.@bridge macros for functions and sets defined outside MOI (#582).
    • Document solver-specific attributes (#580) and implement them in Utilities.CachingOptimizer (#565).

    v0.6.3 (November 16, 2018)

    • Variables and constraints are now allowed to have duplicate names. An error is thrown only on lookup. This change breaks some existing tests. (#549)
    • Attributes may now be partially set (some values could be nothing). (#563)
    • Performance improvements in Utilities.Model (#549, #567, #568)
    • Fix bug in QuadtoSOC (#558).
    • New supports_default_copy_to method that optimizers should implement to control caching behavior.
    • Documentation improvements.

    v0.6.2 (October 26, 2018)

    • Improve hygiene of @model macro (#544).
    • Fix bug in copy tests (#543).
    • Fix bug in UniversalFallback attribute getter (#540).
    • Allow all correct solutions for solve_blank_obj unit test (#537).
    • Add errors for Allocate-Load and bad constraints (#534).
    • [performance] Add specialized implementation of hash for VariableIndex (#533).
    • [performance] Construct the name to object dictionaries lazily in model (#535).
    • Add the QuadtoSOC bridge which transforms ScalarQuadraticFunction constraints into RotatedSecondOrderCone (#483).

    v0.6.1 (September 22, 2018)

    • Enable PositiveSemidefiniteConeSquare set and quadratic functions in MOIB.fullbridgeoptimizer (#524).
    • Add warning in the bridge between PositiveSemidefiniteConeSquare and PositiveSemidefiniteConeTriangle when the matrix is almost symmetric (#522).
    • Modify MOIT.copytest to not add multiples constraints on the same variable (#521).
    • Add missing keyword argument in one of MOIU.add_scalar_constraint methods (#520).

    v0.6.0 (August 30, 2018)

    • The MOIU.@model and MOIB.@bridge macros now support functions and sets defined in external modules. As a consequence, function and set names in the macro arguments need to be prefixed by module name.
    • Rename functions according to the JuMP style guide:
      • copy! with keyword arguments copynames and warnattributes -> copy_to with keyword arguments copy_names and warn_attributes;
      • set! -> set;
      • addvariable[s]! -> add_variable[s];
      • supportsconstraint -> supports_constraint;
      • addconstraint[s]! -> add_constraint[s];
      • isvalid -> is_valid;
      • isempty -> is_empty;
      • Base.delete! -> delete;
      • modify! -> modify;
      • transform! -> transform;
      • initialize! -> initialize;
      • write -> write_to_file; and
      • read! -> read_from_file.
    • Remove free! (use Base.finalize instead).
    • Add the SquarePSD bridge which transforms PositiveSemidefiniteConeTriangle constraints into PositiveSemidefiniteConeTriangle.
    • Add result fallback for ConstraintDual of variable-wise constraint, ConstraintPrimal and ObjectiveValue.
    • Add tests for ObjectiveBound.
    • Add test for empty rows in vector linear constraint.
    • Rework errors: CannotError has been renamed NotAllowedError and the distinction between UnsupportedError and NotAllowedError is now about whether the element is not supported (for example, it cannot be copied a model containing this element) or the operation is not allowed (either because it is not implemented, because it cannot be performed in the current state of the model, or because it cannot be performed for a specific index)
    • canget is removed. NoSolution is added as a result status to indicate that the solver does not have either a primal or dual solution available (See #479).

    v0.5.0 (August 5, 2018)

    • Fix names with CachingOptimizer.
    • Cleanup thanks to @mohamed82008.
    • Added a universal fallback for constraints.
    • Fast utilities for function canonicalization thanks to @rdeits.
    • Renamed dimension field to side_dimension in the context of matrix-like sets.
    • New and improved tests for cases like duplicate terms and ObjectiveBound.
    • Removed cantransform, canaddconstraint, canaddvariable, canset, canmodify, and candelete functions from the API. They are replaced by a new set of errors that are thrown: Subtypes of UnsupportedError indicate unsupported operations, while subtypes of CannotError indicate operations that cannot be performed in the current state.
    • The API for copy! is updated to remove the CopyResult type.
    • Updates for the new JuMP style guide.

    v0.4.1 (June 28, 2018)

    • Fixes vector function modification on 32 bits.
    • Fixes Bellman-Ford algorithm for bridges.
    • Added an NLP test with FeasibilitySense.
    • Update modification documentation.

    v0.4.0 (June 23, 2018)

    • Helper constructors for VectorAffineTerm and VectorQuadraticTerm.
    • Added modify_lhs to TestConfig.
    • Additional unit tests for optimizers.
    • Added a type parameter to CachingOptimizer for the optimizer field.
    • New API for problem modification (#388)
    • Tests pass without deprecation warnings on Julia 0.7.
    • Small fixes and documentation updates.

    v0.3.0 (May 25, 2018)

    • Functions have been redefined to use arrays-of-structs instead of structs-of-arrays.
    • Improvements to MockOptimizer.
    • Significant changes to Bridges.
    • New and improved unit tests.
    • Fixes for Julia 0.7.

    v0.2.0 (April 24, 2018)

    • Improvements to and better coverage of Tests.
    • Documentation fixes.
    • SolverName attribute.
    • Changes to the NLP interface (new definition of variable order and arrays of structs for bound pairs and sparsity patterns).
    • Addition of NLP tests.
    • Introduction of UniversalFallback.
    • copynames keyword argument to MOI.copy!.
    • Add Bridges submodule.

    v0.1.0 (February 28, 2018)

    • Initial public release.
    • The framework for MOI was developed at the JuMP-dev workshop at MIT in June 2017 as a sorely needed replacement for MathProgBase.
    diff --git a/previews/PR3913/moi/developer/checklists/index.html b/previews/PR3913/moi/developer/checklists/index.html index 682fe06e3c1..bf683784e05 100644 --- a/previews/PR3913/moi/developer/checklists/index.html +++ b/previews/PR3913/moi/developer/checklists/index.html @@ -112,4 +112,4 @@ ## Documentation - - [ ] The version fields are updated in `docs/src/submodules/FileFormats/overview.md` + - [ ] The version fields are updated in `docs/src/submodules/FileFormats/overview.md` diff --git a/previews/PR3913/moi/index.html b/previews/PR3913/moi/index.html index 8908c098dd4..c8bbff241b0 100644 --- a/previews/PR3913/moi/index.html +++ b/previews/PR3913/moi/index.html @@ -10,4 +10,4 @@ year={2021}, doi={10.1287/ijoc.2021.1067}, publisher={INFORMS} -}

    A preprint of this paper is freely available.

    +}

    A preprint of this paper is freely available.

    diff --git a/previews/PR3913/moi/manual/constraints/index.html b/previews/PR3913/moi/manual/constraints/index.html index 74cd014ee4b..9a0487aa79a 100644 --- a/previews/PR3913/moi/manual/constraints/index.html +++ b/previews/PR3913/moi/manual/constraints/index.html @@ -23,4 +23,4 @@ false

    Constraint attributes

    The following attributes are available for constraints:

    Get and set these attributes using get and set.

    julia> MOI.set(model, MOI.ConstraintName(), c, "con_c")
 
 julia> MOI.get(model, MOI.ConstraintName(), c)
-"con_c"

    Constraints by function-set pairs

    Below is a list of common constraint types and how they are represented as function-set pairs in MOI. In the notation below, $x$ is a vector of decision variables, $x_i$ is a scalar decision variable, $\alpha, \beta$ are scalar constants, $a, b$ are constant vectors, A is a constant matrix and $\mathbb{R}_+$ (resp. $\mathbb{R}_-$) is the set of non-negative (resp. non-positive) real numbers.

    Linear constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $a^Tx \le \beta$ScalarAffineFunctionLessThan
    $a^Tx \ge \alpha$ScalarAffineFunctionGreaterThan
    $a^Tx = \beta$ScalarAffineFunctionEqualTo
    $\alpha \le a^Tx \le \beta$ScalarAffineFunctionInterval
    $x_i \le \beta$VariableIndexLessThan
    $x_i \ge \alpha$VariableIndexGreaterThan
    $x_i = \beta$VariableIndexEqualTo
    $\alpha \le x_i \le \beta$VariableIndexInterval
    $Ax + b \in \mathbb{R}_+^n$VectorAffineFunctionNonnegatives
    $Ax + b \in \mathbb{R}_-^n$VectorAffineFunctionNonpositives
    $Ax + b = 0$VectorAffineFunctionZeros

    By convention, solvers are not expected to support nonzero constant terms in the ScalarAffineFunctions the first four rows of the preceding table because they are redundant with the parameters of the sets. For example, encode $2x + 1 \le 2$ as $2x \le 1$.

    Constraints with VariableIndex in LessThan, GreaterThan, EqualTo, or Interval sets have a natural interpretation as variable bounds. As such, it is typically not natural to impose multiple lower- or upper-bounds on the same variable, and the solver interfaces will throw respectively LowerBoundAlreadySet or UpperBoundAlreadySet.

    Moreover, adding two VariableIndex constraints on the same variable with the same set is impossible because they share the same index as it is the index of the variable, see ConstraintIndex.

    It is natural, however, to impose upper- and lower-bounds separately as two different constraints on a single variable. The difference between imposing bounds by using a single Interval constraint and by using separate LessThan and GreaterThan constraints is that the latter will allow the solver to return separate dual multipliers for the two bounds, while the former will allow the solver to return only a single dual for the interval constraint.

    Conic constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $\lVert Ax + b\rVert_2 \le c^Tx + d$VectorAffineFunctionSecondOrderCone
    $y \ge \lVert x \rVert_2$VectorOfVariablesSecondOrderCone
    $2yz \ge \lVert x \rVert_2^2, y,z \ge 0$VectorOfVariablesRotatedSecondOrderCone
    $(a_1^Tx + b_1,a_2^Tx + b_2,a_3^Tx + b_3) \in \mathcal{E}$VectorAffineFunctionExponentialCone
    $A(x) \in \mathcal{S}_+$VectorAffineFunctionPositiveSemidefiniteConeTriangle
    $B(x) \in \mathcal{S}_+$VectorAffineFunctionPositiveSemidefiniteConeSquare
    $x \in \mathcal{S}_+$VectorOfVariablesPositiveSemidefiniteConeTriangle
    $x \in \mathcal{S}_+$VectorOfVariablesPositiveSemidefiniteConeSquare

    where $\mathcal{E}$ is the exponential cone (see ExponentialCone), $\mathcal{S}_+$ is the set of positive semidefinite symmetric matrices, $A$ is an affine map that outputs symmetric matrices and $B$ is an affine map that outputs square matrices.

    Quadratic constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $\frac{1}{2}x^TQx + a^Tx + b \ge 0$ScalarQuadraticFunctionGreaterThan
    $\frac{1}{2}x^TQx + a^Tx + b \le 0$ScalarQuadraticFunctionLessThan
    $\frac{1}{2}x^TQx + a^Tx + b = 0$ScalarQuadraticFunctionEqualTo
    Bilinear matrix inequalityVectorQuadraticFunctionPositiveSemidefiniteCone...
    Note

    For more details on the internal format of the quadratic functions see ScalarQuadraticFunction or VectorQuadraticFunction.

    Discrete and logical constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $x_i \in \mathbb{Z}$VariableIndexInteger
    $x_i \in \{0,1\}$VariableIndexZeroOne
    $x_i \in \{0\} \cup [l,u]$VariableIndexSemicontinuous
    $x_i \in \{0\} \cup \{l,l+1,\ldots,u-1,u\}$VariableIndexSemiinteger
    At most one component of $x$ can be nonzeroVectorOfVariablesSOS1
    At most two components of $x$ can be nonzero, and if so they must be adjacent componentsVectorOfVariablesSOS2
    $y = 1 \implies a^T x \in S$VectorAffineFunctionIndicator

    JuMP mapping

    The following bullet points show examples of how JuMP constraints are translated into MOI function-set pairs:

    • @constraint(m, 2x + y <= 10) becomes ScalarAffineFunction-in-LessThan
    • @constraint(m, 2x + y >= 10) becomes ScalarAffineFunction-in-GreaterThan
    • @constraint(m, 2x + y == 10) becomes ScalarAffineFunction-in-EqualTo
    • @constraint(m, 0 <= 2x + y <= 10) becomes ScalarAffineFunction-in-Interval
    • @constraint(m, 2x + y in ArbitrarySet()) becomes ScalarAffineFunction-in-ArbitrarySet.

    Variable bounds are handled in a similar fashion:

    • @variable(m, x <= 1) becomes VariableIndex-in-LessThan
    • @variable(m, x >= 1) becomes VariableIndex-in-GreaterThan

    One notable difference is that a variable with an upper and lower bound is translated into two constraints, rather than an interval, that is:

    • @variable(m, 0 <= x <= 1) becomes VariableIndex-in-LessThan and VariableIndex-in-GreaterThan.
    +"con_c"

    Constraints by function-set pairs

    Below is a list of common constraint types and how they are represented as function-set pairs in MOI. In the notation below, $x$ is a vector of decision variables, $x_i$ is a scalar decision variable, $\alpha, \beta$ are scalar constants, $a, b$ are constant vectors, A is a constant matrix and $\mathbb{R}_+$ (resp. $\mathbb{R}_-$) is the set of non-negative (resp. non-positive) real numbers.

    Linear constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $a^Tx \le \beta$ScalarAffineFunctionLessThan
    $a^Tx \ge \alpha$ScalarAffineFunctionGreaterThan
    $a^Tx = \beta$ScalarAffineFunctionEqualTo
    $\alpha \le a^Tx \le \beta$ScalarAffineFunctionInterval
    $x_i \le \beta$VariableIndexLessThan
    $x_i \ge \alpha$VariableIndexGreaterThan
    $x_i = \beta$VariableIndexEqualTo
    $\alpha \le x_i \le \beta$VariableIndexInterval
    $Ax + b \in \mathbb{R}_+^n$VectorAffineFunctionNonnegatives
    $Ax + b \in \mathbb{R}_-^n$VectorAffineFunctionNonpositives
    $Ax + b = 0$VectorAffineFunctionZeros

    By convention, solvers are not expected to support nonzero constant terms in the ScalarAffineFunctions the first four rows of the preceding table because they are redundant with the parameters of the sets. For example, encode $2x + 1 \le 2$ as $2x \le 1$.

    Constraints with VariableIndex in LessThan, GreaterThan, EqualTo, or Interval sets have a natural interpretation as variable bounds. As such, it is typically not natural to impose multiple lower- or upper-bounds on the same variable, and the solver interfaces will throw respectively LowerBoundAlreadySet or UpperBoundAlreadySet.

    Moreover, adding two VariableIndex constraints on the same variable with the same set is impossible because they share the same index as it is the index of the variable, see ConstraintIndex.

    It is natural, however, to impose upper- and lower-bounds separately as two different constraints on a single variable. The difference between imposing bounds by using a single Interval constraint and by using separate LessThan and GreaterThan constraints is that the latter will allow the solver to return separate dual multipliers for the two bounds, while the former will allow the solver to return only a single dual for the interval constraint.

    Conic constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $\lVert Ax + b\rVert_2 \le c^Tx + d$VectorAffineFunctionSecondOrderCone
    $y \ge \lVert x \rVert_2$VectorOfVariablesSecondOrderCone
    $2yz \ge \lVert x \rVert_2^2, y,z \ge 0$VectorOfVariablesRotatedSecondOrderCone
    $(a_1^Tx + b_1,a_2^Tx + b_2,a_3^Tx + b_3) \in \mathcal{E}$VectorAffineFunctionExponentialCone
    $A(x) \in \mathcal{S}_+$VectorAffineFunctionPositiveSemidefiniteConeTriangle
    $B(x) \in \mathcal{S}_+$VectorAffineFunctionPositiveSemidefiniteConeSquare
    $x \in \mathcal{S}_+$VectorOfVariablesPositiveSemidefiniteConeTriangle
    $x \in \mathcal{S}_+$VectorOfVariablesPositiveSemidefiniteConeSquare

    where $\mathcal{E}$ is the exponential cone (see ExponentialCone), $\mathcal{S}_+$ is the set of positive semidefinite symmetric matrices, $A$ is an affine map that outputs symmetric matrices and $B$ is an affine map that outputs square matrices.

    Quadratic constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $\frac{1}{2}x^TQx + a^Tx + b \ge 0$ScalarQuadraticFunctionGreaterThan
    $\frac{1}{2}x^TQx + a^Tx + b \le 0$ScalarQuadraticFunctionLessThan
    $\frac{1}{2}x^TQx + a^Tx + b = 0$ScalarQuadraticFunctionEqualTo
    Bilinear matrix inequalityVectorQuadraticFunctionPositiveSemidefiniteCone...
    Note

    For more details on the internal format of the quadratic functions see ScalarQuadraticFunction or VectorQuadraticFunction.

    Discrete and logical constraints

    Mathematical ConstraintMOI FunctionMOI Set
    $x_i \in \mathbb{Z}$VariableIndexInteger
    $x_i \in \{0,1\}$VariableIndexZeroOne
    $x_i \in \{0\} \cup [l,u]$VariableIndexSemicontinuous
    $x_i \in \{0\} \cup \{l,l+1,\ldots,u-1,u\}$VariableIndexSemiinteger
    At most one component of $x$ can be nonzeroVectorOfVariablesSOS1
    At most two components of $x$ can be nonzero, and if so they must be adjacent componentsVectorOfVariablesSOS2
    $y = 1 \implies a^T x \in S$VectorAffineFunctionIndicator

    JuMP mapping

    The following bullet points show examples of how JuMP constraints are translated into MOI function-set pairs:

    • @constraint(m, 2x + y <= 10) becomes ScalarAffineFunction-in-LessThan
    • @constraint(m, 2x + y >= 10) becomes ScalarAffineFunction-in-GreaterThan
    • @constraint(m, 2x + y == 10) becomes ScalarAffineFunction-in-EqualTo
    • @constraint(m, 0 <= 2x + y <= 10) becomes ScalarAffineFunction-in-Interval
    • @constraint(m, 2x + y in ArbitrarySet()) becomes ScalarAffineFunction-in-ArbitrarySet.

    Variable bounds are handled in a similar fashion:

    • @variable(m, x <= 1) becomes VariableIndex-in-LessThan
    • @variable(m, x >= 1) becomes VariableIndex-in-GreaterThan

    One notable difference is that a variable with an upper and lower bound is translated into two constraints, rather than an interval, that is:

    • @variable(m, 0 <= x <= 1) becomes VariableIndex-in-LessThan and VariableIndex-in-GreaterThan.
    diff --git a/previews/PR3913/moi/manual/models/index.html b/previews/PR3913/moi/manual/models/index.html index b5c46e2505a..17779111354 100644 --- a/previews/PR3913/moi/manual/models/index.html +++ b/previews/PR3913/moi/manual/models/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Models

    The most significant part of MOI is the definition of the model API that is used to specify an instance of an optimization problem (for example, by adding variables and constraints). Objects that implement the model API must inherit from the ModelLike abstract type.

    Notably missing from the model API is the method to solve an optimization problem. ModelLike objects may store an instance (for example, in memory or backed by a file format) without being linked to a particular solver. In addition to the model API, MOI defines AbstractOptimizer and provides methods to solve the model and interact with solutions. See the Solutions section for more details.

    Info

    Throughout the rest of the manual, model is used as a generic ModelLike, and optimizer is used as a generic AbstractOptimizer.

    Tip

    MOI does not export functions, but for brevity we often omit qualifying names with the MOI module. Best practice is to have

    import MathOptInterface as MOI

    and prefix all MOI methods with MOI. in user code. If a name is also available in base Julia, we always explicitly use the module prefix, for example, with MOI.get.

    Attributes

    Attributes are properties of the model that can be queried and modified. These include constants such as the number of variables in a model NumberOfVariables), and properties of variables and constraints such as the name of a variable (VariableName).

    There are four types of attributes:

    Some attributes are values that can be queried by the user but not modified, while other attributes can be modified by the user.

    All interactions with attributes occur through the get and set functions.

    Consult the docstrings of each attribute for information on what it represents.

    ModelLike API

    The following attributes are available:

    AbstractOptimizer API

    The following attributes are available:

    +
    GitHub

    Models

    The most significant part of MOI is the definition of the model API that is used to specify an instance of an optimization problem (for example, by adding variables and constraints). Objects that implement the model API must inherit from the ModelLike abstract type.

    Notably missing from the model API is the method to solve an optimization problem. ModelLike objects may store an instance (for example, in memory or backed by a file format) without being linked to a particular solver. In addition to the model API, MOI defines AbstractOptimizer and provides methods to solve the model and interact with solutions. See the Solutions section for more details.

    Info

    Throughout the rest of the manual, model is used as a generic ModelLike, and optimizer is used as a generic AbstractOptimizer.

    Tip

    MOI does not export functions, but for brevity we often omit qualifying names with the MOI module. Best practice is to have

    import MathOptInterface as MOI

    and prefix all MOI methods with MOI. in user code. If a name is also available in base Julia, we always explicitly use the module prefix, for example, with MOI.get.

    Attributes

    Attributes are properties of the model that can be queried and modified. These include constants such as the number of variables in a model NumberOfVariables), and properties of variables and constraints such as the name of a variable (VariableName).

    There are four types of attributes:

    Some attributes are values that can be queried by the user but not modified, while other attributes can be modified by the user.

    All interactions with attributes occur through the get and set functions.

    Consult the docstrings of each attribute for information on what it represents.

    ModelLike API

    The following attributes are available:

    AbstractOptimizer API

    The following attributes are available:

    diff --git a/previews/PR3913/moi/manual/modification/index.html b/previews/PR3913/moi/manual/modification/index.html index e11acca8e1e..b1ae9121745 100644 --- a/previews/PR3913/moi/manual/modification/index.html +++ b/previews/PR3913/moi/manual/modification/index.html @@ -152,4 +152,4 @@ ); julia> MOI.get(model, MOI.ConstraintFunction(), c) ≈ new_f -true +true diff --git a/previews/PR3913/moi/manual/solutions/index.html b/previews/PR3913/moi/manual/solutions/index.html index 7ba473dbf42..adba89c011e 100644 --- a/previews/PR3913/moi/manual/solutions/index.html +++ b/previews/PR3913/moi/manual/solutions/index.html @@ -36,4 +36,4 @@ end rethrow(err) # Something else went wrong. Rethrow the error end -end +end diff --git a/previews/PR3913/moi/manual/standard_form/index.html b/previews/PR3913/moi/manual/standard_form/index.html index 1d71aec4282..f8fa110730d 100644 --- a/previews/PR3913/moi/manual/standard_form/index.html +++ b/previews/PR3913/moi/manual/standard_form/index.html @@ -7,4 +7,4 @@ & \min_{x \in \mathbb{R}^n} & f_0(x) \\ & \;\;\text{s.t.} & f_i(x) & \in \mathcal{S}_i & i = 1 \ldots m -\end{align}\]

    where:

    • the functions $f_0, f_1, \ldots, f_m$ are specified by AbstractFunction objects
    • the sets $\mathcal{S}_1, \ldots, \mathcal{S}_m$ are specified by AbstractSet objects
    Tip

    For more information on this standard form, read our paper.

    MOI defines some commonly used functions and sets, but the interface is extensible to other sets recognized by the solver.

    Functions

    The function types implemented in MathOptInterface.jl are:

    FunctionDescription
    VariableIndex$x_j$, the projection onto a single coordinate defined by a variable index $j$.
    VectorOfVariablesThe projection onto multiple coordinates (that is, extracting a sub-vector).
    ScalarAffineFunction$a^T x + b$, where $a$ is a vector and $b$ scalar.
    ScalarNonlinearFunction$f(x)$, where $f$ is a nonlinear function.
    VectorAffineFunction$A x + b$, where $A$ is a matrix and $b$ is a vector.
    ScalarQuadraticFunction$\frac{1}{2} x^T Q x + a^T x + b$, where $Q$ is a symmetric matrix, $a$ is a vector, and $b$ is a constant.
    VectorQuadraticFunctionA vector of scalar-valued quadratic functions.
    VectorNonlinearFunction$f(x)$, where $f$ is a vector-valued nonlinear function.

    Extensions for nonlinear programming are present but not yet well documented.

    One-dimensional sets

    The one-dimensional set types implemented in MathOptInterface.jl are:

    SetDescription
    LessThan(u)$(-\infty, u]$
    GreaterThan(l)$[l, \infty)$
    EqualTo(v)$\{v\}$
    Interval(l, u)$[l, u]$
    Integer()$\mathbb{Z}$
    ZeroOne()$\{ 0, 1 \}$
    Semicontinuous(l, u)$\{ 0\} \cup [l, u]$
    Semiinteger(l, u)$\{ 0\} \cup \{l,l+1,\ldots,u-1,u\}$

    Vector cones

    The vector-valued set types implemented in MathOptInterface.jl are:

    SetDescription
    Reals(d)$\mathbb{R}^{d}$
    Zeros(d)$0^{d}$
    Nonnegatives(d)$\{ x \in \mathbb{R}^{d} : x \ge 0 \}$
    Nonpositives(d)$\{ x \in \mathbb{R}^{d} : x \le 0 \}$
    SecondOrderCone(d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \lVert x \rVert_2 \}$
    RotatedSecondOrderCone(d)$\{ (t,u,x) \in \mathbb{R}^{d} : 2tu \ge \lVert x \rVert_2^2, t \ge 0,u \ge 0 \}$
    ExponentialCone()$\{ (x,y,z) \in \mathbb{R}^3 : y \exp (x/y) \le z, y > 0 \}$
    DualExponentialCone()$\{ (u,v,w) \in \mathbb{R}^3 : -u \exp (v/u) \le \exp(1) w, u < 0 \}$
    GeometricMeanCone(d)$\{ (t,x) \in \mathbb{R}^{1+n} : x \ge 0, t \le \sqrt[n]{x_1 x_2 \cdots x_n} \}$ where $n$ is $d - 1$
    PowerCone(α)$\{ (x,y,z) \in \mathbb{R}^3 : x^{\alpha} y^{1-\alpha} \ge |z|, x \ge 0,y \ge 0 \}$
    DualPowerCone(α)$\{ (u,v,w) \in \mathbb{R}^3 : \left(\frac{u}{\alpha}\right)^{\alpha}\left(\frac{v}{1-\alpha}\right)^{1-\alpha} \ge |w|, u,v \ge 0 \}$
    NormOneCone(d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \sum_i \lvert x_i \rvert \}$
    NormInfinityCone(d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \max_i \lvert x_i \rvert \}$
    RelativeEntropyCone(d)$\{ (u, v, w) \in \mathbb{R}^{d} : u \ge \sum_i w_i \log (\frac{w_i}{v_i}), v_i \ge 0, w_i \ge 0 \}$
    HyperRectangle(l, u)$\{x \in \bar{\mathbb{R}}^d: x_i \in [l_i, u_i] \forall i=1,\ldots,d\}$
    NormCone(p, d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \left(\sum\limits_i \lvert x_i \rvert^p\right)^{\frac{1}{p}} \}$

    Matrix cones

    The matrix-valued set types implemented in MathOptInterface.jl are:

    SetDescription
    RootDetConeTriangle(d)$\{ (t,X) \in \mathbb{R}^{1+d(1+d)/2} : t \le \det(X)^{1/d}, X \mbox{ is the upper triangle of a PSD matrix} \}$
    RootDetConeSquare(d)$\{ (t,X) \in \mathbb{R}^{1+d^2} : t \le \det(X)^{1/d}, X \mbox{ is a PSD matrix} \}$
    PositiveSemidefiniteConeTriangle(d)$\{ X \in \mathbb{R}^{d(d+1)/2} : X \mbox{ is the upper triangle of a PSD matrix} \}$
    PositiveSemidefiniteConeSquare(d)$\{ X \in \mathbb{R}^{d^2} : X \mbox{ is a PSD matrix} \}$
    LogDetConeTriangle(d)$\{ (t,u,X) \in \mathbb{R}^{2+d(1+d)/2} : t \le u\log(\det(X/u)), X \mbox{ is the upper triangle of a PSD matrix}, u > 0 \}$
    LogDetConeSquare(d)$\{ (t,u,X) \in \mathbb{R}^{2+d^2} : t \le u \log(\det(X/u)), X \mbox{ is a PSD matrix}, u > 0 \}$
    NormSpectralCone(r, c)$\{ (t, X) \in \mathbb{R}^{1 + r \times c} : t \ge \sigma_1(X), X \mbox{ is a } r\times c\mbox{ matrix} \}$
    NormNuclearCone(r, c)$\{ (t, X) \in \mathbb{R}^{1 + r \times c} : t \ge \sum_i \sigma_i(X), X \mbox{ is a } r\times c\mbox{ matrix} \}$
    HermitianPositiveSemidefiniteConeTriangle(d)The cone of Hermitian positive semidefinite matrices, with
    side_dimension rows and columns.
    Scaled(S)The set S scaled so that Utilities.set_dot corresponds to LinearAlgebra.dot

    Some of these cones can take two forms: XXXConeTriangle and XXXConeSquare.

    In XXXConeTriangle sets, the matrix is assumed to be symmetric, and the elements are provided by a vector, in which the entries of the upper-right triangular part of the matrix are given column by column (or equivalently, the entries of the lower-left triangular part are given row by row).

    In XXXConeSquare sets, the entries of the matrix are given column by column (or equivalently, row by row), and the matrix is constrained to be symmetric. As an example, given a 2-by-2 matrix of variables X and a one-dimensional variable t, we can specify a root-det constraint as [t, X11, X12, X22] ∈ RootDetConeTriangle or [t, X11, X12, X21, X22] ∈ RootDetConeSquare.

    We provide both forms to enable flexibility for solvers who may natively support one or the other. Transformations between XXXConeTriangle and XXXConeSquare are handled by bridges, which removes the chance of conversion mistakes by users or solver developers.

    Multi-dimensional sets with combinatorial structure

    Other sets are vector-valued, with a particular combinatorial structure. Read their docstrings for more information on how to interpret them.

    SetDescription
    SOS1A Special Ordered Set (SOS) of Type I
    SOS2A Special Ordered Set (SOS) of Type II
    IndicatorA set to specify an indicator constraint
    ComplementsA set to specify a mixed complementarity constraint
    AllDifferentThe all_different global constraint
    BinPackingThe bin_packing global constraint
    CircuitThe circuit global constraint
    CountAtLeastThe at_least global constraint
    CountBelongsThe nvalue global constraint
    CountDistinctThe distinct global constraint
    CountGreaterThanThe count_gt global constraint
    CumulativeThe cumulative global constraint
    PathThe path global constraint
    TableThe table global constraint
    +\end{align}\]

    where:

    • the functions $f_0, f_1, \ldots, f_m$ are specified by AbstractFunction objects
    • the sets $\mathcal{S}_1, \ldots, \mathcal{S}_m$ are specified by AbstractSet objects
    Tip

    For more information on this standard form, read our paper.

    MOI defines some commonly used functions and sets, but the interface is extensible to other sets recognized by the solver.

    Functions

    The function types implemented in MathOptInterface.jl are:

    FunctionDescription
    VariableIndex$x_j$, the projection onto a single coordinate defined by a variable index $j$.
    VectorOfVariablesThe projection onto multiple coordinates (that is, extracting a sub-vector).
    ScalarAffineFunction$a^T x + b$, where $a$ is a vector and $b$ scalar.
    ScalarNonlinearFunction$f(x)$, where $f$ is a nonlinear function.
    VectorAffineFunction$A x + b$, where $A$ is a matrix and $b$ is a vector.
    ScalarQuadraticFunction$\frac{1}{2} x^T Q x + a^T x + b$, where $Q$ is a symmetric matrix, $a$ is a vector, and $b$ is a constant.
    VectorQuadraticFunctionA vector of scalar-valued quadratic functions.
    VectorNonlinearFunction$f(x)$, where $f$ is a vector-valued nonlinear function.

    Extensions for nonlinear programming are present but not yet well documented.

    One-dimensional sets

    The one-dimensional set types implemented in MathOptInterface.jl are:

    SetDescription
    LessThan(u)$(-\infty, u]$
    GreaterThan(l)$[l, \infty)$
    EqualTo(v)$\{v\}$
    Interval(l, u)$[l, u]$
    Integer()$\mathbb{Z}$
    ZeroOne()$\{ 0, 1 \}$
    Semicontinuous(l, u)$\{ 0\} \cup [l, u]$
    Semiinteger(l, u)$\{ 0\} \cup \{l,l+1,\ldots,u-1,u\}$

    Vector cones

    The vector-valued set types implemented in MathOptInterface.jl are:

    SetDescription
    Reals(d)$\mathbb{R}^{d}$
    Zeros(d)$0^{d}$
    Nonnegatives(d)$\{ x \in \mathbb{R}^{d} : x \ge 0 \}$
    Nonpositives(d)$\{ x \in \mathbb{R}^{d} : x \le 0 \}$
    SecondOrderCone(d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \lVert x \rVert_2 \}$
    RotatedSecondOrderCone(d)$\{ (t,u,x) \in \mathbb{R}^{d} : 2tu \ge \lVert x \rVert_2^2, t \ge 0,u \ge 0 \}$
    ExponentialCone()$\{ (x,y,z) \in \mathbb{R}^3 : y \exp (x/y) \le z, y > 0 \}$
    DualExponentialCone()$\{ (u,v,w) \in \mathbb{R}^3 : -u \exp (v/u) \le \exp(1) w, u < 0 \}$
    GeometricMeanCone(d)$\{ (t,x) \in \mathbb{R}^{1+n} : x \ge 0, t \le \sqrt[n]{x_1 x_2 \cdots x_n} \}$ where $n$ is $d - 1$
    PowerCone(α)$\{ (x,y,z) \in \mathbb{R}^3 : x^{\alpha} y^{1-\alpha} \ge |z|, x \ge 0,y \ge 0 \}$
    DualPowerCone(α)$\{ (u,v,w) \in \mathbb{R}^3 : \left(\frac{u}{\alpha}\right)^{\alpha}\left(\frac{v}{1-\alpha}\right)^{1-\alpha} \ge |w|, u,v \ge 0 \}$
    NormOneCone(d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \sum_i \lvert x_i \rvert \}$
    NormInfinityCone(d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \max_i \lvert x_i \rvert \}$
    RelativeEntropyCone(d)$\{ (u, v, w) \in \mathbb{R}^{d} : u \ge \sum_i w_i \log (\frac{w_i}{v_i}), v_i \ge 0, w_i \ge 0 \}$
    HyperRectangle(l, u)$\{x \in \bar{\mathbb{R}}^d: x_i \in [l_i, u_i] \forall i=1,\ldots,d\}$
    NormCone(p, d)$\{ (t,x) \in \mathbb{R}^{d} : t \ge \left(\sum\limits_i \lvert x_i \rvert^p\right)^{\frac{1}{p}} \}$

    Matrix cones

    The matrix-valued set types implemented in MathOptInterface.jl are:

    SetDescription
    RootDetConeTriangle(d)$\{ (t,X) \in \mathbb{R}^{1+d(1+d)/2} : t \le \det(X)^{1/d}, X \mbox{ is the upper triangle of a PSD matrix} \}$
    RootDetConeSquare(d)$\{ (t,X) \in \mathbb{R}^{1+d^2} : t \le \det(X)^{1/d}, X \mbox{ is a PSD matrix} \}$
    PositiveSemidefiniteConeTriangle(d)$\{ X \in \mathbb{R}^{d(d+1)/2} : X \mbox{ is the upper triangle of a PSD matrix} \}$
    PositiveSemidefiniteConeSquare(d)$\{ X \in \mathbb{R}^{d^2} : X \mbox{ is a PSD matrix} \}$
    LogDetConeTriangle(d)$\{ (t,u,X) \in \mathbb{R}^{2+d(1+d)/2} : t \le u\log(\det(X/u)), X \mbox{ is the upper triangle of a PSD matrix}, u > 0 \}$
    LogDetConeSquare(d)$\{ (t,u,X) \in \mathbb{R}^{2+d^2} : t \le u \log(\det(X/u)), X \mbox{ is a PSD matrix}, u > 0 \}$
    NormSpectralCone(r, c)$\{ (t, X) \in \mathbb{R}^{1 + r \times c} : t \ge \sigma_1(X), X \mbox{ is a } r\times c\mbox{ matrix} \}$
    NormNuclearCone(r, c)$\{ (t, X) \in \mathbb{R}^{1 + r \times c} : t \ge \sum_i \sigma_i(X), X \mbox{ is a } r\times c\mbox{ matrix} \}$
    HermitianPositiveSemidefiniteConeTriangle(d)The cone of Hermitian positive semidefinite matrices, with
    side_dimension rows and columns.
    Scaled(S)The set S scaled so that Utilities.set_dot corresponds to LinearAlgebra.dot

    Some of these cones can take two forms: XXXConeTriangle and XXXConeSquare.

    In XXXConeTriangle sets, the matrix is assumed to be symmetric, and the elements are provided by a vector, in which the entries of the upper-right triangular part of the matrix are given column by column (or equivalently, the entries of the lower-left triangular part are given row by row).

    In XXXConeSquare sets, the entries of the matrix are given column by column (or equivalently, row by row), and the matrix is constrained to be symmetric. As an example, given a 2-by-2 matrix of variables X and a one-dimensional variable t, we can specify a root-det constraint as [t, X11, X12, X22] ∈ RootDetConeTriangle or [t, X11, X12, X21, X22] ∈ RootDetConeSquare.

    We provide both forms to enable flexibility for solvers who may natively support one or the other. Transformations between XXXConeTriangle and XXXConeSquare are handled by bridges, which removes the chance of conversion mistakes by users or solver developers.

    Multi-dimensional sets with combinatorial structure

    Other sets are vector-valued, with a particular combinatorial structure. Read their docstrings for more information on how to interpret them.

    SetDescription
    SOS1A Special Ordered Set (SOS) of Type I
    SOS2A Special Ordered Set (SOS) of Type II
    IndicatorA set to specify an indicator constraint
    ComplementsA set to specify a mixed complementarity constraint
    AllDifferentThe all_different global constraint
    BinPackingThe bin_packing global constraint
    CircuitThe circuit global constraint
    CountAtLeastThe at_least global constraint
    CountBelongsThe nvalue global constraint
    CountDistinctThe distinct global constraint
    CountGreaterThanThe count_gt global constraint
    CumulativeThe cumulative global constraint
    PathThe path global constraint
    TableThe table global constraint
    diff --git a/previews/PR3913/moi/manual/variables/index.html b/previews/PR3913/moi/manual/variables/index.html index 2e49b87c025..7c90d3bd121 100644 --- a/previews/PR3913/moi/manual/variables/index.html +++ b/previews/PR3913/moi/manual/variables/index.html @@ -14,4 +14,4 @@ false
    Warning

    Not all ModelLike models support deleting variables. A DeleteNotAllowed error is thrown if this is not supported.

    Variable attributes

    The following attributes are available for variables:

    Get and set these attributes using get and set.

    julia> MOI.set(model, MOI.VariableName(), x, "var_x")
 
 julia> MOI.get(model, MOI.VariableName(), x)
-"var_x"
    +"var_x" diff --git a/previews/PR3913/moi/reference/callbacks/index.html b/previews/PR3913/moi/reference/callbacks/index.html index 5b9f792cc48..7d39b8a3433 100644 --- a/previews/PR3913/moi/reference/callbacks/index.html +++ b/previews/PR3913/moi/reference/callbacks/index.html @@ -33,4 +33,4 @@ MOI.submit(optimizer, MOI.HeuristicSolution(callback_data), x, values) end -endsource
    MathOptInterface.HeuristicSolution — Type
    HeuristicSolution(callback_data)

    Heuristically obtained feasible solution. The solution is submitted as variables, values where values[i] gives the value of variables[i], similarly to set. The submit call returns a HeuristicSolutionStatus indicating whether the provided solution was accepted or rejected.

    This can be submitted only from the HeuristicCallback. The field callback_data is a solver-specific callback type that is passed as the argument to the heuristic callback.

    Some solvers require a complete solution, others only partial solutions.

    source
    +endsource
    MathOptInterface.HeuristicSolution — Type
    HeuristicSolution(callback_data)

    Heuristically obtained feasible solution. The solution is submitted as variables, values where values[i] gives the value of variables[i], similarly to set. The submit call returns a HeuristicSolutionStatus indicating whether the provided solution was accepted or rejected.

    This can be submitted only from the HeuristicCallback. The field callback_data is a solver-specific callback type that is passed as the argument to the heuristic callback.

    Some solvers require a complete solution, others only partial solutions.

    source
    diff --git a/previews/PR3913/moi/reference/constraints/index.html b/previews/PR3913/moi/reference/constraints/index.html index 95784400b42..61969a7a652 100644 --- a/previews/PR3913/moi/reference/constraints/index.html +++ b/previews/PR3913/moi/reference/constraints/index.html @@ -44,4 +44,4 @@ model::ModelLike, ::Type{F}, ::Type{S}, -)::Bool where {F<:AbstractFunction,S<:AbstractSet}

    Return a Bool indicating whether model supports F-in-S constraints, that is, copy_to(model, src) does not throw UnsupportedConstraint when src contains F-in-S constraints. If F-in-S constraints are only not supported in specific circumstances, for example, F-in-S constraints cannot be combined with another type of constraint, it should still return true.

    source

    Attributes

    MathOptInterface.ConstraintName — Type
    ConstraintName()

    A constraint attribute for a string identifying the constraint.

    It is valid for constraints variables to have the same name; however, constraints with duplicate names cannot be looked up using get, regardless of whether they have the same F-in-S type.

    ConstraintName has a default value of "" if not set.

    Notes

    You should not implement ConstraintName for VariableIndex constraints.

    source
    MathOptInterface.ConstraintPrimal — Type
    ConstraintPrimal(result_index::Int = 1)

    A constraint attribute for the assignment to some constraint's primal value in result result_index.

    If the constraint is f(x) in S, then in most cases the ConstraintPrimal is the value of f, evaluated at the corresponding VariablePrimal solution.

    However, some conic solvers reformulate b - Ax in S to s = b - Ax, s in S. These solvers may return the value of s for ConstraintPrimal, rather than b - Ax. (Although these are constrained by an equality constraint, due to numerical tolerances they may not be identical.)

    If the solver does not have a primal value for the constraint because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ConstraintPrimal attribute.

    If result_index is omitted, it is 1 by default. See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.ConstraintDual — Type
    ConstraintDual(result_index::Int = 1)

    A constraint attribute for the assignment to some constraint's dual value in result result_index. If result_index is omitted, it is 1 by default.

    If the solver does not have a dual value for the variable because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a primal solution is available), the result is undefined. Users should first check DualStatus before accessing the ConstraintDual attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.ConstraintBasisStatus — Type
    ConstraintBasisStatus(result_index::Int = 1)

    A constraint attribute for the BasisStatusCode of some constraint in result result_index, with respect to an available optimal solution basis. If result_index is omitted, it is 1 by default.

    If the solver does not have a basis status for the constraint because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ConstraintBasisStatus attribute.

    See ResultCount for information on how the results are ordered.

    Notes

    For the basis status of a variable, query VariableBasisStatus.

    ConstraintBasisStatus does not apply to VariableIndex constraints. You can infer the basis status of a VariableIndex constraint by looking at the result of VariableBasisStatus.

    source
    MathOptInterface.ConstraintFunction — Type
    ConstraintFunction()

    A constraint attribute for the AbstractFunction object used to define the constraint.

    It is guaranteed to be equivalent but not necessarily identical to the function provided by the user.

    source
    MathOptInterface.CanonicalConstraintFunction — Type
    CanonicalConstraintFunction()

    A constraint attribute for a canonical representation of the AbstractFunction object used to define the constraint.

    Getting this attribute is guaranteed to return a function that is equivalent but not necessarily identical to the function provided by the user.

    By default, MOI.get(model, MOI.CanonicalConstraintFunction(), ci) fallbacks to MOI.Utilities.canonical(MOI.get(model, MOI.ConstraintFunction(), ci)). However, if model knows that the constraint function is canonical then it can implement a specialized method that directly return the function without calling Utilities.canonical. Therefore, the value returned cannot be assumed to be a copy of the function stored in model. Moreover, Utilities.Model checks with Utilities.is_canonical whether the function stored internally is already canonical and if it's the case, then it returns the function stored internally instead of a copy.

    source
    MathOptInterface.BasisStatusCode — Type
    BasisStatusCode

    An Enum of possible values for the ConstraintBasisStatus and VariableBasisStatus attributes, explaining the status of a given element with respect to an optimal solution basis.

    Notes

    • NONBASIC_AT_LOWER and NONBASIC_AT_UPPER should be used only for constraints with the Interval set. In this case, they are necessary to distinguish which side of the constraint is active. One-sided constraints (for example, LessThan and GreaterThan) should use NONBASIC instead of the NONBASIC_AT_* values. This restriction does not apply to VariableBasisStatus, which should return NONBASIC_AT_* regardless of whether the alternative bound exists.

    • In linear programs, SUPER_BASIC occurs when a variable with no bounds is not in the basis.

    Values

    Possible values are:

    source
    +)::Bool where {F<:AbstractFunction,S<:AbstractSet}

    Return a Bool indicating whether model supports F-in-S constraints, that is, copy_to(model, src) does not throw UnsupportedConstraint when src contains F-in-S constraints. If F-in-S constraints are only not supported in specific circumstances, for example, F-in-S constraints cannot be combined with another type of constraint, it should still return true.

    source

    Attributes

    MathOptInterface.ConstraintName — Type
    ConstraintName()

    A constraint attribute for a string identifying the constraint.

    It is valid for constraints variables to have the same name; however, constraints with duplicate names cannot be looked up using get, regardless of whether they have the same F-in-S type.

    ConstraintName has a default value of "" if not set.

    Notes

    You should not implement ConstraintName for VariableIndex constraints.

    source
    MathOptInterface.ConstraintPrimal — Type
    ConstraintPrimal(result_index::Int = 1)

    A constraint attribute for the assignment to some constraint's primal value in result result_index.

    If the constraint is f(x) in S, then in most cases the ConstraintPrimal is the value of f, evaluated at the corresponding VariablePrimal solution.

    However, some conic solvers reformulate b - Ax in S to s = b - Ax, s in S. These solvers may return the value of s for ConstraintPrimal, rather than b - Ax. (Although these are constrained by an equality constraint, due to numerical tolerances they may not be identical.)

    If the solver does not have a primal value for the constraint because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ConstraintPrimal attribute.

    If result_index is omitted, it is 1 by default. See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.ConstraintDual — Type
    ConstraintDual(result_index::Int = 1)

    A constraint attribute for the assignment to some constraint's dual value in result result_index. If result_index is omitted, it is 1 by default.

    If the solver does not have a dual value for the variable because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a primal solution is available), the result is undefined. Users should first check DualStatus before accessing the ConstraintDual attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.ConstraintBasisStatus — Type
    ConstraintBasisStatus(result_index::Int = 1)

    A constraint attribute for the BasisStatusCode of some constraint in result result_index, with respect to an available optimal solution basis. If result_index is omitted, it is 1 by default.

    If the solver does not have a basis status for the constraint because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ConstraintBasisStatus attribute.

    See ResultCount for information on how the results are ordered.

    Notes

    For the basis status of a variable, query VariableBasisStatus.

    ConstraintBasisStatus does not apply to VariableIndex constraints. You can infer the basis status of a VariableIndex constraint by looking at the result of VariableBasisStatus.

    source
    MathOptInterface.ConstraintFunction — Type
    ConstraintFunction()

    A constraint attribute for the AbstractFunction object used to define the constraint.

    It is guaranteed to be equivalent but not necessarily identical to the function provided by the user.

    source
    MathOptInterface.CanonicalConstraintFunction — Type
    CanonicalConstraintFunction()

    A constraint attribute for a canonical representation of the AbstractFunction object used to define the constraint.

    Getting this attribute is guaranteed to return a function that is equivalent but not necessarily identical to the function provided by the user.

    By default, MOI.get(model, MOI.CanonicalConstraintFunction(), ci) fallbacks to MOI.Utilities.canonical(MOI.get(model, MOI.ConstraintFunction(), ci)). However, if model knows that the constraint function is canonical then it can implement a specialized method that directly return the function without calling Utilities.canonical. Therefore, the value returned cannot be assumed to be a copy of the function stored in model. Moreover, Utilities.Model checks with Utilities.is_canonical whether the function stored internally is already canonical and if it's the case, then it returns the function stored internally instead of a copy.

    source
    MathOptInterface.BasisStatusCode — Type
    BasisStatusCode

    An Enum of possible values for the ConstraintBasisStatus and VariableBasisStatus attributes, explaining the status of a given element with respect to an optimal solution basis.

    Notes

    • NONBASIC_AT_LOWER and NONBASIC_AT_UPPER should be used only for constraints with the Interval set. In this case, they are necessary to distinguish which side of the constraint is active. One-sided constraints (for example, LessThan and GreaterThan) should use NONBASIC instead of the NONBASIC_AT_* values. This restriction does not apply to VariableBasisStatus, which should return NONBASIC_AT_* regardless of whether the alternative bound exists.

    • In linear programs, SUPER_BASIC occurs when a variable with no bounds is not in the basis.

    Values

    Possible values are:

    source
    diff --git a/previews/PR3913/moi/reference/errors/index.html b/previews/PR3913/moi/reference/errors/index.html index 7f0824b3b3d..607ab7e78fd 100644 --- a/previews/PR3913/moi/reference/errors/index.html +++ b/previews/PR3913/moi/reference/errors/index.html @@ -57,4 +57,4 @@ julia> throw(MOI.UnsupportedNonlinearOperator(:black_box)) ERROR: MathOptInterface.UnsupportedNonlinearOperator: The nonlinear operator `:black_box` is not supported by the model. Stacktrace: -[...]source

    Note that setting the ConstraintFunction of a VariableIndex constraint is not allowed:

    +[...]source

    Note that setting the ConstraintFunction of a VariableIndex constraint is not allowed:

    diff --git a/previews/PR3913/moi/reference/models/index.html b/previews/PR3913/moi/reference/models/index.html index f9d95c14b9f..aec809f9baf 100644 --- a/previews/PR3913/moi/reference/models/index.html +++ b/previews/PR3913/moi/reference/models/index.html @@ -7,7 +7,7 @@ model::MOI.ModelLike, attr::MOI.AbstractConstraintAttribute, bridge::AbstractBridge, -)

    Return the value of the attribute attr of the model model for the constraint bridged by bridge.

    source
    get(model::GenericModel, attr::MathOptInterface.AbstractOptimizerAttribute)

    Return the value of the attribute attr from the model's MOI backend.

    source
    get(model::GenericModel, attr::MathOptInterface.AbstractModelAttribute)

    Return the value of the attribute attr from the model's MOI backend.

    source
    get(optimizer::AbstractOptimizer, attr::AbstractOptimizerAttribute)

    Return an attribute attr of the optimizer optimizer.

    get(model::ModelLike, attr::AbstractModelAttribute)

    Return an attribute attr of the model model.

    get(model::ModelLike, attr::AbstractVariableAttribute, v::VariableIndex)

    If the attribute attr is set for the variable v in the model model, return its value, return nothing otherwise. If the attribute attr is not supported by model then an error should be thrown instead of returning nothing.

    get(model::ModelLike, attr::AbstractVariableAttribute, v::Vector{VariableIndex})

    Return a vector of attributes corresponding to each variable in the collection v in the model model.

    get(model::ModelLike, attr::AbstractConstraintAttribute, c::ConstraintIndex)

    If the attribute attr is set for the constraint c in the model model, return its value, return nothing otherwise. If the attribute attr is not supported by model then an error should be thrown instead of returning nothing.

    get(
+)

    Return the value of the attribute attr of the model model for the constraint bridged by bridge.

    source
    get(model::GenericModel, attr::MathOptInterface.AbstractOptimizerAttribute)

    Return the value of the attribute attr from the model's MOI backend.

    source
    get(model::GenericModel, attr::MathOptInterface.AbstractModelAttribute)

    Return the value of the attribute attr from the model's MOI backend.

    source
    get(optimizer::AbstractOptimizer, attr::AbstractOptimizerAttribute)

    Return an attribute attr of the optimizer optimizer.

    get(model::ModelLike, attr::AbstractModelAttribute)

    Return an attribute attr of the model model.

    get(model::ModelLike, attr::AbstractVariableAttribute, v::VariableIndex)

    If the attribute attr is set for the variable v in the model model, return its value, return nothing otherwise. If the attribute attr is not supported by model then an error should be thrown instead of returning nothing.

    get(model::ModelLike, attr::AbstractVariableAttribute, v::Vector{VariableIndex})

    Return a vector of attributes corresponding to each variable in the collection v in the model model.

    get(model::ModelLike, attr::AbstractConstraintAttribute, c::ConstraintIndex)

    If the attribute attr is set for the constraint c in the model model, return its value, return nothing otherwise. If the attribute attr is not supported by model then an error should be thrown instead of returning nothing.

    get(
     model::ModelLike,
     attr::AbstractConstraintAttribute,
     c::Vector{ConstraintIndex{F,S}},
@@ -139,4 +139,4 @@
 MOI.get(model, MOI.RelativeGapTolerance())  # returns 1e-3
 # ... and the relative gap of the obtained solution is smaller or equal to the
 # tolerance
-MOI.get(model, MOI.RelativeGap())  # should return something ≤ 1e-3
    Warning

    The mathematical definition of "relative gap", and its allowed range, are solver-dependent. Typically, solvers expect a value between 0.0 and 1.0.

    source

    List of attributes useful for optimizers

    MathOptInterface.TerminationStatusCode — Type
    TerminationStatusCode

    An Enum of possible values for the TerminationStatus attribute. This attribute is meant to explain the reason why the optimizer stopped executing in the most recent call to optimize!.

    Values

    Possible values are:

    • OPTIMIZE_NOT_CALLED: The algorithm has not started.
    • OPTIMAL: The algorithm found a globally optimal solution.
    • INFEASIBLE: The algorithm concluded that no feasible solution exists.
    • DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.
    • LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.
    • LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.
    • INFEASIBLE_OR_UNBOUNDED: The algorithm stopped because it decided that the problem is infeasible or unbounded; this occasionally happens during MIP presolve.
    • ALMOST_OPTIMAL: The algorithm found a globally optimal solution to relaxed tolerances.
    • ALMOST_INFEASIBLE: The algorithm concluded that no feasible solution exists within relaxed tolerances.
    • ALMOST_DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem within relaxed tolerances.
    • ALMOST_LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, or could not find directions for improvement within relaxed tolerances.
    • ITERATION_LIMIT: An iterative algorithm stopped after conducting the maximum number of iterations.
    • TIME_LIMIT: The algorithm stopped after a user-specified computation time.
    • NODE_LIMIT: A branch-and-bound algorithm stopped because it explored a maximum number of nodes in the branch-and-bound tree.
    • SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.
    • MEMORY_LIMIT: The algorithm stopped because it ran out of memory.
    • OBJECTIVE_LIMIT: The algorithm stopped because it found a solution better than a minimum limit set by the user.
    • NORM_LIMIT: The algorithm stopped because the norm of an iterate became too large.
    • OTHER_LIMIT: The algorithm stopped due to a limit not covered by one of the _LIMIT_ statuses above.
    • SLOW_PROGRESS: The algorithm stopped because it was unable to continue making progress towards the solution.
    • NUMERICAL_ERROR: The algorithm stopped because it encountered unrecoverable numerical error.
    • INVALID_MODEL: The algorithm stopped because the model is invalid.
    • INVALID_OPTION: The algorithm stopped because it was provided an invalid option.
    • INTERRUPTED: The algorithm stopped because of an interrupt signal.
    • OTHER_ERROR: The algorithm stopped because of an error not covered by one of the statuses defined above.
    source
    MathOptInterface.DUAL_INFEASIBLE — Constant
    DUAL_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.

    source
    MathOptInterface.LOCALLY_SOLVED — Constant
    LOCALLY_SOLVED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.

    source
    MathOptInterface.LOCALLY_INFEASIBLE — Constant
    LOCALLY_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.

    source
    MathOptInterface.SOLUTION_LIMIT — Constant
    SOLUTION_LIMIT::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.

    source
    MathOptInterface.DualStatus — Type
    DualStatus(result_index::Int = 1)

    A model attribute for the ResultStatusCode of the dual result result_index. If result_index is omitted, it defaults to 1.

    See ResultCount for information on how the results are ordered.

    If result_index is larger than the value of ResultCount then NO_SOLUTION is returned.

    source
    MathOptInterface.ResultCount — Type
    ResultCount()

    A model attribute for the number of results available.

    Order of solutions

    A number of attributes contain an index, result_index, which is used to refer to one of the available results. Thus, result_index must be an integer between 1 and the number of available results.

    As a general rule, the first result (result_index=1) is the most important result (for example, an optimal solution or an infeasibility certificate). Other results will typically be alternate solutions that the solver found during the search for the first result.

    If a (local) optimal solution is available, that is, TerminationStatus is OPTIMAL or LOCALLY_SOLVED, the first result must correspond to the (locally) optimal solution. Other results may be alternative optimal solutions, or they may be other suboptimal solutions; use ObjectiveValue to distinguish between them.

    If a primal or dual infeasibility certificate is available, that is, TerminationStatus is INFEASIBLE or DUAL_INFEASIBLE and the corresponding PrimalStatus or DualStatus is INFEASIBILITY_CERTIFICATE, then the first result must be a certificate. Other results may be alternate certificates, or infeasible points.

    source
    MathOptInterface.ObjectiveValue — Type
    ObjectiveValue(result_index::Int = 1)

    A model attribute for the objective value of the primal solution result_index.

    If the solver does not have a primal value for the objective because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ObjectiveValue attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.DualObjectiveValue — Type
    DualObjectiveValue(result_index::Int = 1)

    A model attribute for the value of the objective function of the dual problem for the result_indexth dual result.

    If the solver does not have a dual value for the objective because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a primal solution is available), the result is undefined. Users should first check DualStatus before accessing the DualObjectiveValue attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.RelativeGap — Type
    RelativeGap()

    A model attribute for the final relative optimality gap.

    Warning

    The definition of this gap is solver-dependent. However, most solvers implementing this attribute define the relative gap as some variation of $\frac{|b-f|}{|f|}$, where $b$ is the best bound and $f$ is the best feasible objective value.

    source
    MathOptInterface.SimplexIterations — Type
    SimplexIterations()

    A model attribute for the cumulative number of simplex iterations during the optimization process.

    For a mixed-integer program (MIP), the return value is the total simplex iterations for all nodes.

    source
    MathOptInterface.NodeCount — Type
    NodeCount()

    A model attribute for the total number of branch-and-bound nodes explored while solving a mixed-integer program (MIP).

    source

    ResultStatusCode

    MathOptInterface.ResultStatusCode — Type
    ResultStatusCode

    An Enum of possible values for the PrimalStatus and DualStatus attributes.

    The values indicate how to interpret the result vector.

    Values

    Possible values are:

    • NO_SOLUTION: the result vector is empty.
    • FEASIBLE_POINT: the result vector is a feasible point.
    • NEARLY_FEASIBLE_POINT: the result vector is feasible if some constraint tolerances are relaxed.
    • INFEASIBLE_POINT: the result vector is an infeasible point.
    • INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.
    • NEARLY_INFEASIBILITY_CERTIFICATE: the result satisfies a relaxed criterion for a certificate of infeasibility.
    • REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.
    • NEARLY_REDUCTION_CERTIFICATE: the result satisfies a relaxed criterion for an ill-posed certificate.
    • UNKNOWN_RESULT_STATUS: the result vector contains a solution with an unknown interpretation.
    • OTHER_RESULT_STATUS: the result vector contains a solution with an interpretation not covered by one of the statuses defined above
    source
    MathOptInterface.INFEASIBILITY_CERTIFICATE — Constant
    INFEASIBILITY_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.

    source
    MathOptInterface.REDUCTION_CERTIFICATE — Constant
    REDUCTION_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.

    source

    Conflict Status

    MathOptInterface.compute_conflict! — Function
    compute_conflict!(optimizer::AbstractOptimizer)

    Computes a minimal subset of constraints such that the model with the other constraint removed is still infeasible.

    Some solvers call a set of conflicting constraints an Irreducible Inconsistent Subsystem (IIS).

    See also ConflictStatus and ConstraintConflictStatus.

    Note

    If the model is modified after a call to compute_conflict!, the implementor is not obliged to purge the conflict. Any calls to the above attributes may return values for the original conflict without a warning. Similarly, when modifying the model, the conflict can be discarded.

    source
    MathOptInterface.ConflictStatusCode — Type
    ConflictStatusCode

    An Enum of possible values for the ConflictStatus attribute. This attribute is meant to explain the reason why the conflict finder stopped executing in the most recent call to compute_conflict!.

    Possible values are:

    • COMPUTE_CONFLICT_NOT_CALLED: the function compute_conflict! has not yet been called
    • NO_CONFLICT_EXISTS: there is no conflict because the problem is feasible
    • NO_CONFLICT_FOUND: the solver could not find a conflict
    • CONFLICT_FOUND: at least one conflict could be found
    source
    MathOptInterface.ConflictParticipationStatusCode — Type
    ConflictParticipationStatusCode

    An Enum of possible values for the ConstraintConflictStatus attribute. This attribute is meant to indicate whether a given constraint participates or not in the last computed conflict.

    Values

    Possible values are:

    • NOT_IN_CONFLICT: the constraint does not participate in the conflict
    • IN_CONFLICT: the constraint participates in the conflict
    • MAYBE_IN_CONFLICT: the constraint may participate in the conflict, the solver was not able to prove that the constraint can be excluded from the conflict
    source
    +MOI.get(model, MOI.RelativeGap()) # should return something ≤ 1e-3
    Warning

    The mathematical definition of "relative gap", and its allowed range, are solver-dependent. Typically, solvers expect a value between 0.0 and 1.0.

    source

    List of attributes useful for optimizers

    MathOptInterface.TerminationStatusCode — Type
    TerminationStatusCode

    An Enum of possible values for the TerminationStatus attribute. This attribute is meant to explain the reason why the optimizer stopped executing in the most recent call to optimize!.

    Values

    Possible values are:

    • OPTIMIZE_NOT_CALLED: The algorithm has not started.
    • OPTIMAL: The algorithm found a globally optimal solution.
    • INFEASIBLE: The algorithm concluded that no feasible solution exists.
    • DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.
    • LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.
    • LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.
    • INFEASIBLE_OR_UNBOUNDED: The algorithm stopped because it decided that the problem is infeasible or unbounded; this occasionally happens during MIP presolve.
    • ALMOST_OPTIMAL: The algorithm found a globally optimal solution to relaxed tolerances.
    • ALMOST_INFEASIBLE: The algorithm concluded that no feasible solution exists within relaxed tolerances.
    • ALMOST_DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem within relaxed tolerances.
    • ALMOST_LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, or could not find directions for improvement within relaxed tolerances.
    • ITERATION_LIMIT: An iterative algorithm stopped after conducting the maximum number of iterations.
    • TIME_LIMIT: The algorithm stopped after a user-specified computation time.
    • NODE_LIMIT: A branch-and-bound algorithm stopped because it explored a maximum number of nodes in the branch-and-bound tree.
    • SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.
    • MEMORY_LIMIT: The algorithm stopped because it ran out of memory.
    • OBJECTIVE_LIMIT: The algorithm stopped because it found a solution better than a minimum limit set by the user.
    • NORM_LIMIT: The algorithm stopped because the norm of an iterate became too large.
    • OTHER_LIMIT: The algorithm stopped due to a limit not covered by one of the _LIMIT_ statuses above.
    • SLOW_PROGRESS: The algorithm stopped because it was unable to continue making progress towards the solution.
    • NUMERICAL_ERROR: The algorithm stopped because it encountered unrecoverable numerical error.
    • INVALID_MODEL: The algorithm stopped because the model is invalid.
    • INVALID_OPTION: The algorithm stopped because it was provided an invalid option.
    • INTERRUPTED: The algorithm stopped because of an interrupt signal.
    • OTHER_ERROR: The algorithm stopped because of an error not covered by one of the statuses defined above.
    source
    MathOptInterface.DUAL_INFEASIBLE — Constant
    DUAL_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    DUAL_INFEASIBLE: The algorithm concluded that no dual bound exists for the problem. If, additionally, a feasible (primal) solution is known to exist, this status typically implies that the problem is unbounded, with some technical exceptions.

    source
    MathOptInterface.LOCALLY_SOLVED — Constant
    LOCALLY_SOLVED::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_SOLVED: The algorithm converged to a stationary point, local optimal solution, could not find directions for improvement, or otherwise completed its search without global guarantees.

    source
    MathOptInterface.LOCALLY_INFEASIBLE — Constant
    LOCALLY_INFEASIBLE::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    LOCALLY_INFEASIBLE: The algorithm converged to an infeasible point or otherwise completed its search without finding a feasible solution, without guarantees that no feasible solution exists.

    source
    MathOptInterface.SOLUTION_LIMIT — Constant
    SOLUTION_LIMIT::TerminationStatusCode

    An instance of the TerminationStatusCode enum.

    SOLUTION_LIMIT: The algorithm stopped because it found the required number of solutions. This is often used in MIPs to get the solver to return the first feasible solution it encounters.

    source
    MathOptInterface.DualStatus — Type
    DualStatus(result_index::Int = 1)

    A model attribute for the ResultStatusCode of the dual result result_index. If result_index is omitted, it defaults to 1.

    See ResultCount for information on how the results are ordered.

    If result_index is larger than the value of ResultCount then NO_SOLUTION is returned.

    source
    MathOptInterface.ResultCount — Type
    ResultCount()

    A model attribute for the number of results available.

    Order of solutions

    A number of attributes contain an index, result_index, which is used to refer to one of the available results. Thus, result_index must be an integer between 1 and the number of available results.

    As a general rule, the first result (result_index=1) is the most important result (for example, an optimal solution or an infeasibility certificate). Other results will typically be alternate solutions that the solver found during the search for the first result.

    If a (local) optimal solution is available, that is, TerminationStatus is OPTIMAL or LOCALLY_SOLVED, the first result must correspond to the (locally) optimal solution. Other results may be alternative optimal solutions, or they may be other suboptimal solutions; use ObjectiveValue to distinguish between them.

    If a primal or dual infeasibility certificate is available, that is, TerminationStatus is INFEASIBLE or DUAL_INFEASIBLE and the corresponding PrimalStatus or DualStatus is INFEASIBILITY_CERTIFICATE, then the first result must be a certificate. Other results may be alternate certificates, or infeasible points.

    source
    MathOptInterface.ObjectiveValue — Type
    ObjectiveValue(result_index::Int = 1)

    A model attribute for the objective value of the primal solution result_index.

    If the solver does not have a primal value for the objective because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the ObjectiveValue attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.DualObjectiveValue — Type
    DualObjectiveValue(result_index::Int = 1)

    A model attribute for the value of the objective function of the dual problem for the result_indexth dual result.

    If the solver does not have a dual value for the objective because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a primal solution is available), the result is undefined. Users should first check DualStatus before accessing the DualObjectiveValue attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.RelativeGap — Type
    RelativeGap()

    A model attribute for the final relative optimality gap.

    Warning

    The definition of this gap is solver-dependent. However, most solvers implementing this attribute define the relative gap as some variation of $\frac{|b-f|}{|f|}$, where $b$ is the best bound and $f$ is the best feasible objective value.

    source
    MathOptInterface.SimplexIterations — Type
    SimplexIterations()

    A model attribute for the cumulative number of simplex iterations during the optimization process.

    For a mixed-integer program (MIP), the return value is the total simplex iterations for all nodes.

    source
    MathOptInterface.NodeCount — Type
    NodeCount()

    A model attribute for the total number of branch-and-bound nodes explored while solving a mixed-integer program (MIP).

    source

    ResultStatusCode

    MathOptInterface.ResultStatusCode — Type
    ResultStatusCode

    An Enum of possible values for the PrimalStatus and DualStatus attributes.

    The values indicate how to interpret the result vector.

    Values

    Possible values are:

    • NO_SOLUTION: the result vector is empty.
    • FEASIBLE_POINT: the result vector is a feasible point.
    • NEARLY_FEASIBLE_POINT: the result vector is feasible if some constraint tolerances are relaxed.
    • INFEASIBLE_POINT: the result vector is an infeasible point.
    • INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.
    • NEARLY_INFEASIBILITY_CERTIFICATE: the result satisfies a relaxed criterion for a certificate of infeasibility.
    • REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.
    • NEARLY_REDUCTION_CERTIFICATE: the result satisfies a relaxed criterion for an ill-posed certificate.
    • UNKNOWN_RESULT_STATUS: the result vector contains a solution with an unknown interpretation.
    • OTHER_RESULT_STATUS: the result vector contains a solution with an interpretation not covered by one of the statuses defined above
    source
    MathOptInterface.INFEASIBILITY_CERTIFICATE — Constant
    INFEASIBILITY_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    INFEASIBILITY_CERTIFICATE: the result vector is an infeasibility certificate. If the PrimalStatus is INFEASIBILITY_CERTIFICATE, then the primal result vector is a certificate of dual infeasibility. If the DualStatus is INFEASIBILITY_CERTIFICATE, then the dual result vector is a proof of primal infeasibility.

    source
    MathOptInterface.REDUCTION_CERTIFICATE — Constant
    REDUCTION_CERTIFICATE::ResultStatusCode

    An instance of the ResultStatusCode enum.

    REDUCTION_CERTIFICATE: the result vector is an ill-posed certificate; see this article for details. If the PrimalStatus is REDUCTION_CERTIFICATE, then the primal result vector is a proof that the dual problem is ill-posed. If the DualStatus is REDUCTION_CERTIFICATE, then the dual result vector is a proof that the primal is ill-posed.

    source

    Conflict Status

    MathOptInterface.compute_conflict! — Function
    compute_conflict!(optimizer::AbstractOptimizer)

    Computes a minimal subset of constraints such that the model with the other constraint removed is still infeasible.

    Some solvers call a set of conflicting constraints an Irreducible Inconsistent Subsystem (IIS).

    See also ConflictStatus and ConstraintConflictStatus.

    Note

    If the model is modified after a call to compute_conflict!, the implementor is not obliged to purge the conflict. Any calls to the above attributes may return values for the original conflict without a warning. Similarly, when modifying the model, the conflict can be discarded.

    source
    MathOptInterface.ConflictStatusCode — Type
    ConflictStatusCode

    An Enum of possible values for the ConflictStatus attribute. This attribute is meant to explain the reason why the conflict finder stopped executing in the most recent call to compute_conflict!.

    Possible values are:

    • COMPUTE_CONFLICT_NOT_CALLED: the function compute_conflict! has not yet been called
    • NO_CONFLICT_EXISTS: there is no conflict because the problem is feasible
    • NO_CONFLICT_FOUND: the solver could not find a conflict
    • CONFLICT_FOUND: at least one conflict could be found
    source
    MathOptInterface.ConflictParticipationStatusCode — Type
    ConflictParticipationStatusCode

    An Enum of possible values for the ConstraintConflictStatus attribute. This attribute is meant to indicate whether a given constraint participates or not in the last computed conflict.

    Values

    Possible values are:

    • NOT_IN_CONFLICT: the constraint does not participate in the conflict
    • IN_CONFLICT: the constraint participates in the conflict
    • MAYBE_IN_CONFLICT: the constraint may participate in the conflict, the solver was not able to prove that the constraint can be excluded from the conflict
    source
    diff --git a/previews/PR3913/moi/reference/modification/index.html b/previews/PR3913/moi/reference/modification/index.html index 433acb07c3d..9ad0b155751 100644 --- a/previews/PR3913/moi/reference/modification/index.html +++ b/previews/PR3913/moi/reference/modification/index.html @@ -97,4 +97,4 @@ )

    A struct used to request a change in the quadratic coefficient of a ScalarQuadraticFunction.

    Scaling factors

    A ScalarQuadraticFunction has an implicit 0.5 scaling factor in front of the Q matrix. This modification applies to terms in the Q matrix.

    If variable_1 == variable_2, this modification sets the corresponding diagonal element of the Q matrix to new_coefficient.

    If variable_1 != variable_2, this modification is equivalent to setting both the corresponding upper- and lower-triangular elements of the Q matrix to new_coefficient.

    As a consequence:

    • to modify the term x^2 to become 2x^2, new_coefficient must be 4
    • to modify the term xy to become 2xy, new_coefficient must be 2
    source +) where {T}

    A struct used to request a change in the linear coefficients of a single variable in a vector-valued function.

    New coefficients are specified by (output_index, coefficient) tuples.

    Applicable to VectorAffineFunction and VectorQuadraticFunction.

    source diff --git a/previews/PR3913/moi/reference/nonlinear/index.html b/previews/PR3913/moi/reference/nonlinear/index.html index 03bcc057dcf..9ef9ec21b21 100644 --- a/previews/PR3913/moi/reference/nonlinear/index.html +++ b/previews/PR3913/moi/reference/nonlinear/index.html @@ -425,4 +425,4 @@ :(x[MOI.VariableIndex(1)] * x[MOI.VariableIndex(2)] * x[MOI.VariableIndex(3)] * x[MOI.VariableIndex(4)] >= 25.0) julia> MOI.constraint_expr(evaluator, 2) -:(x[MOI.VariableIndex(1)] ^ 2 + x[MOI.VariableIndex(2)] ^ 2 + x[MOI.VariableIndex(3)] ^ 2 + x[MOI.VariableIndex(4)] ^ 2 == 40.0)source +:(x[MOI.VariableIndex(1)] ^ 2 + x[MOI.VariableIndex(2)] ^ 2 + x[MOI.VariableIndex(3)] ^ 2 + x[MOI.VariableIndex(4)] ^ 2 == 40.0)source diff --git a/previews/PR3913/moi/reference/standard_form/index.html b/previews/PR3913/moi/reference/standard_form/index.html index e44d6576b3a..425e1c000ad 100644 --- a/previews/PR3913/moi/reference/standard_form/index.html +++ b/previews/PR3913/moi/reference/standard_form/index.html @@ -944,4 +944,4 @@ MOI.VectorOfVariables([t; vec(X)]), MOI.RootDetConeSquare(2), ) -MathOptInterface.ConstraintIndex{MathOptInterface.VectorOfVariables, MathOptInterface.RootDetConeSquare}(1)source +MathOptInterface.ConstraintIndex{MathOptInterface.VectorOfVariables, MathOptInterface.RootDetConeSquare}(1)source diff --git a/previews/PR3913/moi/reference/variables/index.html b/previews/PR3913/moi/reference/variables/index.html index 1c9c10098f1..73ccbe85055 100644 --- a/previews/PR3913/moi/reference/variables/index.html +++ b/previews/PR3913/moi/reference/variables/index.html @@ -63,4 +63,4 @@ )::Bool

    Return a Bool indicating whether model supports constraining a variable to belong to a set of type S either on creation of the variable with add_constrained_variable or after the variable is created with add_constraint.

    By default, this function falls back to supports_add_constrained_variables(model, Reals) && supports_constraint(model, MOI.VariableIndex, S) which is the correct definition for most models.

    Example

    Suppose that a solver supports only two kind of variables: binary variables and continuous variables with a lower bound. If the solver decides not to support VariableIndex-in-Binary and VariableIndex-in-GreaterThan constraints, it only has to implement add_constrained_variable for these two sets which prevents the user to add both a binary constraint and a lower bound on the same variable. Moreover, if the user adds a VariableIndex-in-GreaterThan constraint, implementing this interface (that is, supports_add_constrained_variables) enables the constraint to be transparently bridged into a supported constraint.

    source
    MathOptInterface.supports_add_constrained_variables — Function
    supports_add_constrained_variables(
     model::ModelLike,
     S::Type{<:AbstractVectorSet}
-)::Bool

    Return a Bool indicating whether model supports constraining a vector of variables to belong to a set of type S either on creation of the vector of variables with add_constrained_variables or after the variable is created with add_constraint.

    By default, if S is Reals then this function returns true and otherwise, it falls back to supports_add_constrained_variables(model, Reals) && supports_constraint(model, MOI.VectorOfVariables, S) which is the correct definition for most models.

    Example

    In the standard conic form (see Duality), the variables are grouped into several cones and the constraints are affine equality constraints. If Reals is not one of the cones supported by the solvers then it needs to implement supports_add_constrained_variables(::Optimizer, ::Type{Reals}) = false as free variables are not supported. The solvers should then implement supports_add_constrained_variables(::Optimizer, ::Type{<:SupportedCones}) = true where SupportedCones is the union of all cone types that are supported; it does not have to implement the method supports_constraint(::Type{VectorOfVariables}, Type{<:SupportedCones}) as it should return false and it's the default. This prevents the user to constrain the same variable in two different cones. When a VectorOfVariables-in-S is added, the variables of the vector have already been created so they already belong to given cones. If bridges are enabled, the constraint will therefore be bridged by adding slack variables in S and equality constraints ensuring that the slack variables are equal to the corresponding variables of the given constraint function.

    Note that there may also be sets for which !supports_add_constrained_variables(model, S) and supports_constraint(model, MOI.VectorOfVariables, S). For instance, suppose a solver supports positive semidefinite variable constraints and two types of variables: binary variables and nonnegative variables. Then the solver should support adding VectorOfVariables-in-PositiveSemidefiniteConeTriangle constraints, but it should not support creating variables constrained to belong to the PositiveSemidefiniteConeTriangle because the variables in PositiveSemidefiniteConeTriangle should first be created as either binary or non-negative.

    source
    MathOptInterface.is_valid — Method
    is_valid(model::ModelLike, index::Index)::Bool

    Return a Bool indicating whether this index refers to a valid object in the model model.

    source
    MathOptInterface.delete — Method
    delete(model::ModelLike, index::Index)

    Delete the referenced object from the model. Throw DeleteNotAllowed if if index cannot be deleted.

    The following modifications also take effect if Index is VariableIndex:

    • If index used in the objective function, it is removed from the function, that is, it is substituted for zero.
    • For each func-in-set constraint of the model:
      • If func isa VariableIndex and func == index then the constraint is deleted.
      • If func isa VectorOfVariables and index in func.variables then
        • if length(func.variables) == 1 is one, the constraint is deleted;
        • if length(func.variables) > 1 and supports_dimension_update(set) then then the variable is removed from func and set is replaced by update_dimension(set, MOI.dimension(set) - 1).
        • Otherwise, a DeleteNotAllowed error is thrown.
      • Otherwise, the variable is removed from func, that is, it is substituted for zero.
    source
    MathOptInterface.delete — Method
    delete(model::ModelLike, indices::Vector{R<:Index}) where {R}

    Delete the referenced objects in the vector indices from the model. It may be assumed that R is a concrete type. The default fallback sequentially deletes the individual items in indices, although specialized implementations may be more efficient.

    source

    Attributes

    MathOptInterface.VariableName — Type
    VariableName()

    A variable attribute for a string identifying the variable. It is valid for two variables to have the same name; however, variables with duplicate names cannot be looked up using get. It has a default value of "" if not set`.

    source
    MathOptInterface.VariablePrimalStart — Type
    VariablePrimalStart()

    A variable attribute for the initial assignment to some primal variable's value that the optimizer may use to warm-start the solve. May be a number or nothing (unset).

    source
    MathOptInterface.VariablePrimal — Type
    VariablePrimal(result_index::Int = 1)

    A variable attribute for the assignment to some primal variable's value in result result_index. If result_index is omitted, it is 1 by default.

    If the solver does not have a primal value for the variable because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the VariablePrimal attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.VariableBasisStatus — Type
    VariableBasisStatus(result_index::Int = 1)

    A variable attribute for the BasisStatusCode of a variable in result result_index, with respect to an available optimal solution basis.

    If the solver does not have a basis status for the variable because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the VariableBasisStatus attribute.

    See ResultCount for information on how the results are ordered.

    source
    +)::Bool

    Return a Bool indicating whether model supports constraining a vector of variables to belong to a set of type S either on creation of the vector of variables with add_constrained_variables or after the variable is created with add_constraint.

    By default, if S is Reals then this function returns true and otherwise, it falls back to supports_add_constrained_variables(model, Reals) && supports_constraint(model, MOI.VectorOfVariables, S) which is the correct definition for most models.

    Example

    In the standard conic form (see Duality), the variables are grouped into several cones and the constraints are affine equality constraints. If Reals is not one of the cones supported by the solvers then it needs to implement supports_add_constrained_variables(::Optimizer, ::Type{Reals}) = false as free variables are not supported. The solvers should then implement supports_add_constrained_variables(::Optimizer, ::Type{<:SupportedCones}) = true where SupportedCones is the union of all cone types that are supported; it does not have to implement the method supports_constraint(::Type{VectorOfVariables}, Type{<:SupportedCones}) as it should return false and it's the default. This prevents the user to constrain the same variable in two different cones. When a VectorOfVariables-in-S is added, the variables of the vector have already been created so they already belong to given cones. If bridges are enabled, the constraint will therefore be bridged by adding slack variables in S and equality constraints ensuring that the slack variables are equal to the corresponding variables of the given constraint function.

    Note that there may also be sets for which !supports_add_constrained_variables(model, S) and supports_constraint(model, MOI.VectorOfVariables, S). For instance, suppose a solver supports positive semidefinite variable constraints and two types of variables: binary variables and nonnegative variables. Then the solver should support adding VectorOfVariables-in-PositiveSemidefiniteConeTriangle constraints, but it should not support creating variables constrained to belong to the PositiveSemidefiniteConeTriangle because the variables in PositiveSemidefiniteConeTriangle should first be created as either binary or non-negative.

    source
    MathOptInterface.is_valid — Method
    is_valid(model::ModelLike, index::Index)::Bool

    Return a Bool indicating whether this index refers to a valid object in the model model.

    source
    MathOptInterface.delete — Method
    delete(model::ModelLike, index::Index)

    Delete the referenced object from the model. Throw DeleteNotAllowed if if index cannot be deleted.

    The following modifications also take effect if Index is VariableIndex:

    • If index used in the objective function, it is removed from the function, that is, it is substituted for zero.
    • For each func-in-set constraint of the model:
      • If func isa VariableIndex and func == index then the constraint is deleted.
      • If func isa VectorOfVariables and index in func.variables then
        • if length(func.variables) == 1 is one, the constraint is deleted;
        • if length(func.variables) > 1 and supports_dimension_update(set) then then the variable is removed from func and set is replaced by update_dimension(set, MOI.dimension(set) - 1).
        • Otherwise, a DeleteNotAllowed error is thrown.
      • Otherwise, the variable is removed from func, that is, it is substituted for zero.
    source
    MathOptInterface.delete — Method
    delete(model::ModelLike, indices::Vector{R<:Index}) where {R}

    Delete the referenced objects in the vector indices from the model. It may be assumed that R is a concrete type. The default fallback sequentially deletes the individual items in indices, although specialized implementations may be more efficient.

    source

    Attributes

    MathOptInterface.VariableName — Type
    VariableName()

    A variable attribute for a string identifying the variable. It is valid for two variables to have the same name; however, variables with duplicate names cannot be looked up using get. It has a default value of "" if not set`.

    source
    MathOptInterface.VariablePrimalStart — Type
    VariablePrimalStart()

    A variable attribute for the initial assignment to some primal variable's value that the optimizer may use to warm-start the solve. May be a number or nothing (unset).

    source
    MathOptInterface.VariablePrimal — Type
    VariablePrimal(result_index::Int = 1)

    A variable attribute for the assignment to some primal variable's value in result result_index. If result_index is omitted, it is 1 by default.

    If the solver does not have a primal value for the variable because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the VariablePrimal attribute.

    See ResultCount for information on how the results are ordered.

    source
    MathOptInterface.VariableBasisStatus — Type
    VariableBasisStatus(result_index::Int = 1)

    A variable attribute for the BasisStatusCode of a variable in result result_index, with respect to an available optimal solution basis.

    If the solver does not have a basis status for the variable because the result_index is beyond the available solutions (whose number is indicated by the ResultCount attribute), getting this attribute must throw a ResultIndexBoundsError. Otherwise, if the result is unavailable for another reason (for instance, only a dual solution is available), the result is undefined. Users should first check PrimalStatus before accessing the VariableBasisStatus attribute.

    See ResultCount for information on how the results are ordered.

    source
    diff --git a/previews/PR3913/moi/release_notes/index.html b/previews/PR3913/moi/release_notes/index.html index 12f810c6cf1..f1be83c9cac 100644 --- a/previews/PR3913/moi/release_notes/index.html +++ b/previews/PR3913/moi/release_notes/index.html @@ -31,4 +31,4 @@ end write(path, s) end -end

    v0.9.22 (May 22, 2021)

    This release contains backports from the ongoing development of the v0.10 release.

    • Improved type inference in Utilities, Bridges and FileFormats submodules to reduce latency.
    • Improved performance of Utilities.is_canonical.
    • Fixed Utilities.pass_nonvariable_constraints with bridged variables.
    • Fixed performance regression of Utilities.Model.
    • Fixed ordering of objective setting in parser.

    v0.9.21 (April 23, 2021)

    • Added supports_shift_constant.
    • Improve performance of bridging quadratic constraints.
    • Add precompilation statements.
    • Large improvements to the documentation.
    • Fix a variety of inference issues, benefiting precompilation and reducing initial latency.
    • RawParameters are now ignored when resetting a CachingOptimizer. Previously, changing the underlying optimizer after RawParameters were set would throw an error.
    • Utilities.AbstractModel is being refactored. This may break users interacting with private fields of a model generated using @model.

    v0.9.20 (February 20, 2021)

    • Improved performance of Utilities.ScalarFunctionIterator
    • Added support for compute_conflict to MOI layers
    • Added test with zero off-diagonal quadratic term in objective
    • Fixed double deletion of nested bridged SingleVariable/VectorOfVariables constraints
    • Fixed modification of un-set objective
    • Fixed function modification with duplicate terms
    • Made unit tests abort without failing if the problem class is not supported
    • Formatted code with JuliaFormatter
    • Clarified BasisStatusCode's docstring

    v0.9.19 (December 1, 2020)

    • Added CallbackNodeStatus attribute
    • Added bridge from GreaterThan or LessThan to Interval
    • Added tests for infeasibility certificates and double optimize
    • Fixed support for Julia v1.6
    • Re-organized MOI docs and added documentation for adding a test

    v0.9.18 (November 3, 2020)

    • Various improvements for working with complex numbers
    • Added GeoMeantoRelEntrBridge to bridge a GeometricMeanCone constraint to a relative entropy constraint

    v0.9.17 (September 21, 2020)

    • Fixed CleverDict with variable of negative index value
    • Implement supports_add_constrained_variable for MockOptimizer

    v0.9.16 (September 17, 2020)

    • Various fixes:
      • 32-bit support
      • CleverDict with abstract value type
      • Checks in test suite

    v0.9.15 (September 14, 2020)

    • Bridges improvements:
      • (R)SOCtoNonConvexQuad bridge
      • ZeroOne bridge
      • Use supports_add_constrained_variable in LazyBridgeOptimizer
      • Exposed VariableBridgeCost and ConstraintBridgeCost attributes
      • Prioritize constraining variables on creation according to these costs
      • Refactor bridge debugging
    • Large performance improvements across all submodules
    • Lots of documentation improvements
    • FileFormats improvements:
      • Update MathOptFormat to v0.5
      • Fix supported objectives in FileFormats
    • Testing improvements:
      • Add name option for basic_constraint_test
    • Bug fixes and missing methods
      • Add length for iterators
      • Fix bug with duplicate terms
      • Fix order of LinearOfConstraintIndices

    v0.9.14 (May 30, 2020)

    • Add a solver-independent interface for accessing the set of conflicting constraints an Irreducible Inconsistent Subsystem (#1056).
    • Bump JSONSchema dependency from v0.2 to v0.3 (#1090).
    • Documentation improvements:
      • Fix typos (#1054, #1060, #1061, #1064, #1069, #1070).
      • Remove the outdated recommendation for a package implementing MOI for a solver XXX to be called MathOptInterfaceXXX (#1087).
    • Utilities improvements:
      • Fix is_canonical for quadratic functions (#1081, #1089).
      • Implement add_constrained_variable[s] for CachingOptimizer so that it is added as constrained variables to the underlying optimizer (#1084).
      • Add support for custom objective functions for UniversalFallback (#1086).
      • Deterministic ordering of constraints in UniversalFallback (#1088).
    • Testing improvements:
      • Add NormOneCone/NormInfinityCone tests (#1045).
    • Bridges improvements:
      • Add bridges from Semiinteger and Semicontinuous (#1059).
      • Implement getting ConstraintSet for Variable.FlipSignBridge (#1066).
      • Fix setting ConstraintFunction for Constraint.ScalarizeBridge (#1093).
      • Fix NormOne/NormInf bridges with nonzero constants (#1045).
      • Fix StackOverflow in debug (#1063).
    • FileFormats improvements:
      • [SDPA] Implement the extension for integer variables (#1079).
      • [SDPA] Ignore comments after m and nblocks and detect dat-s extension (#1077).
      • [SDPA] No scaling of off-diagonal coefficient (#1076).
      • [SDPA] Add missing negation of constant (#1075).

    v0.9.13 (March 24, 2020)

    • Added tests for Semicontinuous and Semiinteger variables (#1033).
    • Added tests for using ExprGraphs from NLP evaluators (#1043).
    • Update version compatibilities of dependencies (#1034, #1051, #1052).
    • Fixed typos in documentation (#1044).

    v0.9.12 (February 28, 2020)

    • Fixed writing NLPBlock in MathOptFormat (#1037).
    • Fixed MockOptimizer for result attributes with non-one result index (#1039).
    • Updated test template with instantiate (#1032).

    v0.9.11 (February 21, 2020)

    • Add an option for the model created by Utilities.@model to be a subtype of AbstractOptimizer (#1031).
    • Described dual cone in docstrings of GeoMeanCone and RelativeEntropyCone (#1018, #1028).
    • Fixed typos in documentation (#1022, #1024).
    • Fixed warning of unsupported attribute (#1027).
    • Added more rootdet/logdet conic tests (#1026).
    • Implemented ConstraintDual for Constraint.GeoMeanBridge, Constraint.RootDetBridge and Constraint.LogDetBridge and test duals in tests with GeoMeanCone and RootDetConeTriangle and LogDetConeTriangle cones (#1025, #1026).

    v0.9.10 (January 31, 2020)

    • Added OptimizerWithAttributes grouping an optimizer constructor and a list of optimizer attributes (#1008).
    • Added RelativeEntropyCone with corresponding bridge into exponential cone constraints (#993).
    • Added NormSpectralCone and NormNuclearCone with corresponding bridges into positive semidefinite constraints (#976).
    • Added supports_constrained_variable(s) (#1004).
    • Added dual_set_type (#1002).
    • Added tests for vector specialized version of delete (#989, #1011).
    • Added PSD3 test (#1007).
    • Clarified dual solution of Tests.pow1v and Tests.pow1f (#1013).
    • Added support for EqualTo and Zero in Bridges.Constraint.SplitIntervalBridge (#1005).
    • Fixed Utilities.vectorize for empty vector (#1003).
    • Fixed free variables in LP writer (#1006).

    v0.9.9 (December 29, 2019)

    • Incorporated MathOptFormat.jl as the FileFormats submodule. FileFormats provides readers and writers for a number of standard file formats and MOF, a file format specialized for MOI (#969).
    • Improved performance of deletion of vector of variables in MOI.Utilities.Model (#983).
    • Updated to MutableArithmetics v0.2 (#981).
    • Added MutableArithmetics.promote_operation allocation tests (#975).
    • Fixed inference issue on Julia v1.1 (#982).

    v0.9.8 (December 19, 2019)

    • Implemented MutableArithmetics API (#924).
    • Fixed callbacks with CachingOptimizer (#959).
    • Fixed MOI.dimension for MOI.Complements (#948).
    • Added fallback for add_variables (#972).
    • Added is_diagonal_vectorized_index utility (#965).
    • Improved linear constraints display in manual (#963, #964).
    • Bridges improvements:
      • Added IndicatorSet to SOS1 bridge (#877).
      • Added support for starting values for Variable.VectorizeBridge (#944).
      • Fixed MOI.add_constraints with non-bridged variable constraint on bridged variable (#951).
      • Fixed corner cases and docstring of GeoMeanBridge (#961, #962, #966).
      • Fixed choice between variable or constraint bridges for constrained variables (#973).
      • Improve performance of bridge shortest path (#945, #946, #956).
      • Added docstring for test_delete_bridge (#954).
      • Added Variable bridge tests (#952).

    v0.9.7 (October 30, 2019)

    • Implemented _result_index_field for NLPBlockDual (#934).
    • Fixed copy of model with starting values for vector constraints (#941).
    • Bridges improvements:
      • Improved performance of add_bridge and added has_bridge (#935).
      • Added AbstractSetMapBridge for bridges between sets S1, S2 such that there is a linear map A such that A*S1 = S2 (#933).
      • Added support for starting values for FlipSignBridge, VectorizeBridge, ScalarizeBridge, SlackBridge, SplitIntervalBridge, RSOCBridge, SOCRBridge NormInfinityBridge, SOCtoPSDBridge and RSOCtoPSDBridge (#933, #936, #937, #938, #939).

    v0.9.6 (October 25, 2019)

    • Added complementarity constraints (#913).
    • Allowed ModelLike objects as value of attributes (#928).
    • Testing improvements:
      • Added dual_objective_value option to MOI.Test.TestConfig (#922).
      • Added InvalidIndex tests in basic_constraint_tests (#921).
      • Added tests for the constant term in indicator constraint (#929).
    • Bridges improvements:
      • Added support for starting values for Functionize bridges (#923).
      • Added variable indices context to variable bridges (#920).
      • Fixed a typo in printing o debug_supports (#927).

    v0.9.5 (October 9, 2019)

    • Clarified PrimalStatus/DualStatus to be NO_SOLUTION if result_index is out of bounds (#912).
    • Added tolerance for checks and use ResultCount + 1 for the result_index in MOI.Test.solve_result_status (#910, #917).
    • Use 0.5 instead of 2.0 for power in PowerCone in basic_constraint_test (#916).
    • Bridges improvements:
      • Added debug utilities for unsupported variable/constraint/objective (#861).
      • Fixed deletion of variables in bridged VectorOfVariables constraints (#909).
      • Fixed result_index with objective bridges (#911).

    v0.9.4 (October 2, 2019)

    • Added solver-independent MIP callbacks (#782).
    • Implements submit for Utilities.CachingOptimizer and Bridges.AbstractBridgeOptimizer (#906).
    • Added tests for result count of solution attributes (#901, #904).
    • Added NumberOfThreads attribute (#892).
    • Added Utilities.get_bounds to get the bounds on a variable (#890).
    • Added a note on duplicate coefficients in documentation (#581).
    • Added result index in ConstraintBasisStatus (#898).
    • Added extension dictionary to Utilities.Model (#884, #895).
    • Fixed deletion of constrained variables for CachingOptimizer (#905).
    • Implemented Utilities.shift_constraint for Test.UnknownScalarSet (#896).
    • Bridges improvements:
      • Added Variable.RSOCtoSOCBridge (#907).
      • Implemented MOI.get for ConstraintFunction/ConstraintSet for Bridges.Constraint.SquareBridge (#899).

    v0.9.3 (September 20, 2019)

    • Fixed ambiguity detected in Julia v1.3 (#891, #893).
    • Fixed missing sets from ListOfSupportedConstraints (#880).
    • Fixed copy of VectorOfVariables constraints with duplicate indices (#886).
    • Added extension dictionary to MOIU.Model (#884).
    • Implemented MOI.get for function and set for GeoMeanBridge (#888).
    • Updated documentation for SingleVariable indices and bridges (#885).
    • Testing improvements:
      • Added more comprehensive tests for names (#882).
      • Added tests for SingleVariable duals (#883).
      • Added tests for DualExponentialCone and DualPowerCone (#873).
    • Improvements for arbitrary coefficient type:
      • Fixed == for sets with mutable fields (#887).
      • Removed some Float64 assumptions in bridges (#878).
      • Automatic selection of Constraint.[Scalar|Vector]FunctionizeBridge (#889).

    v0.9.2 (September 5, 2019)

    • Implemented model printing for MOI.ModelLike and specialized it for models defined in MOI (864).
    • Generalized contlinear tests for arbitrary coefficient type (#855).
    • Fixed supports_constraint for Semiinteger and Semicontinuous and supports for ObjectiveFunction (#859).
    • Fixed Allocate-Load copy for single variable constraints (#856).
    • Bridges improvements:
      • Add objective bridges (#789).
      • Fixed Variable.RSOCtoPSDBridge for dimension 2 (#869).
      • Added Variable.SOCtoRSOCBridge (#865).
      • Added Constraint.SOCRBridge and disable MOI.Bridges.Constraint.SOCtoPSDBridge (#751).
      • Fixed added_constraint_types for Contraint.LogDetBridge and Constraint.RootDetBridge (#870).

    v0.9.1 (August 22, 2019)

    • Fix support for Julia v1.2 (#834).
    • L1 and L∞ norm epigraph cones and corresponding bridges to LP were added (#818).
    • Added tests to MOI.Test.nametest (#833).
    • Fix MOI.Test.soc3test for solvers not supporting infeasibility certificates (#839).
    • Implements operate for operators * and / between vector function and constant (#837).
    • Implements show for MOI.Utilities.IndexMap (#847).
    • Fix corner cases for mapping of variables in MOI.Utilities.CachingOptimizer and substitution of variables in MOI.Bridges.AbstractBridgeOptimizer (#848).
    • Fix transformation of constant terms for MOI.Bridges.Constraint.SOCtoPSDBridge and MOI.Bridges.Constraint.RSOCtoPSDBridge (#840).

    v0.9.0 (August 13, 2019)

    • Support for Julia v0.6 and v0.7 was dropped (#714, #717).
    • A MOI.Utilities.Model implementation of ModelLike, this should replace most use cases of MOI.Utilities.@model (#781).
    • add_constrained_variable and add_constrained_variables were added (#759).
    • Support for indicator constraints was added (#709, #712).
    • DualObjectiveValue attribute was added (#473).
    • RawParameter attribute was added (#733).
    • A dual_set function was added (#804).
    • A Benchmarks submodule was added to facilitate solver benchmarking (#769).
    • A submit function was added, this may for instance allow the user to submit solutions or cuts to the solver from a callback (#775).
    • The field of ObjectiveValue was renamed to result_index (#729).
    • The _constant and Utilities.getconstant function were renamed to constant
    • REDUCTION_CERTIFICATE result status was added (#734).
    • Abstract matrix sets were added (#731).
    • Testing improvements:
      • The testing guideline was updated (#728).
      • Quadratic tests were added (#697).
      • Unit tests for RawStatusString, SolveTime, Silent and SolverName were added (#726, #741).
      • A rotated second-order cone test was added (#759).
      • A power cone test was added (#768).
      • Tests for ZeroOne variables with variable bounds were added (#772).
      • An unbounded test was added (#773).
      • Existing tests had a few updates (#702, #703, #763).
    • Documentation improvements:
      • Added a section on CachingOptimizer (#777).
      • Added a section on UniversalFallback, Model and @model (#762).
      • Transition the knapsack example to a doctest with MockOptimizer (#786).
    • Utilities improvements:
      • A CleverDict utility was added for a vector that automatically transform into a dictionary once a first index is removed (#767).
      • The Utilities.constant function was renamed to Utilities.constant_vector (#740).
      • Implement optimizer attributes for CachingOptimizer (#745).
      • Rename Utilities.add_scalar_constraint to Utilities.normalize_and_add_constraint (#801).
      • operate with vcat, SingleVariable and VectorOfVariables now returns a VectorOfVariables (#616).
      • Fix a type piracy of operate (#784).
      • The load_constraint fallback signature was fixed (#760).
      • The set_dot function was extended to work with sparse arrays (#805).
    • Bridges improvements:
      • The bridges no longer store the constraint function and set before it is bridged, the bridges now have to implement ConstraintFunction and ConstraintSet if the user wants to recover them. As a consequence, the @bridge macro was removed (#722).
      • Bridge are now instantiated with a bridge_constraint function instead of using a constructor (#730).
      • Fix constraint attributes for bridges (#699).
      • Constraint bridges were moved to the Bridges/Constraint submodule so they should now inherit from MOI.Bridges.Constraint.Abstract and should implement MOI.Bridges.Constraint.concrete_bridge_type instead of MOI.Bridges.concrete_bridge_type (#756).
      • Variable bridges were added in (#759).
      • Various improvements (#746, #747).

    v0.8.4 (March 13, 2019)

    • Performance improvement in default_copy_to and bridge optimizer (#696).
    • Add Silent and implement setting optimizer attributes in caching and mock optimizers (#695).
    • Add Functionize bridges (SingleVariable and VectorOfVariables) (#659).
    • Minor typo fixes (#694).

    v0.8.3 (March 6, 2019)

    • Use zero constant in scalar constraint function of MOI.Test.copytest (#691).
    • Fix variable deletion with SingleVariable objective function (#690).
    • Fix LazyBridgeOptimizer with bridges that add no constraints (#689).
    • Error message improvements (#673, #685, #686, #688).
    • Documentation improvements (#682, #683, #687).
    • Basis status:
      • Remove VariableBasisStatus (#679).
      • Test ConstraintBasisStatus and implement it in bridges (#678).
    • Fix inference of NumberOfVariables and NumberOfConstraints (#677).
    • Implement division between a quadratic function and a number (#675).

    v0.8.2 (February 7, 2019)

    • Add RawStatusString attribute (#629).
    • Do not set names to the optimizer but only to the cache in CachingOptimizer (#638).
    • Make scalar MOI functions act as scalars in broadcast (#646).
    • Add function utilities:
      • Implement Base.zero (#634), Base.iszero (#643), add missing arithmetic operations (#644, #645) and fix division (#648).
      • Add a vectorize function that turns a vector of ScalarAffineFunction into a VectorAffineFunction (#642).
    • Improve support for starting values:
      • Show a warning in copy when starting values are not supported instead of throwing an error (#630).
      • Fix UniversalFallback for getting an variable or constraint attribute set to no indices (#623).
      • Add a test in contlineartest with partially set VariablePrimalStart.
    • Bridges improvements:
      • Fix StackOverFlow in LazyBridgeOptimizer when there is a cycle in the graph of bridges.
      • Add Slack bridges (#610, #650).
      • Add FlipSign bridges (#658).
    • Add tests with duplicate coefficients in ScalarAffineFunction and VectorAffineFunction (#639).
    • Use tolerance to compare VariablePrimal in rotatedsoc1 test (#632).
    • Use a zero constant in ScalarAffineFunction of constraints in psdt2 (#622).

    v0.8.1 (January 7, 2019)

    • Adding an NLP objective now overrides any objective set using the ObjectiveFunction attribute (#619).
    • Rename fullbridgeoptimizer into full_bridge_optimizer (#621).
    • Allow custom constraint types with full_bridge_optimizer (#617).
    • Add Vectorize bridge which transforms scalar linear constraints into vector linear constraints (#615).

    v0.8.0 (December 18, 2018)

    • Rename all enum values to follow the JuMP naming guidelines for constants, for example, Optimal becomes OPTIMAL, and DualInfeasible becomes DUAL_INFEASIBLE.
    • Rename CachingOptimizer methods for style compliance.
    • Add an MOI.TerminationStatusCode called ALMOST_DUAL_INFEASIBLE.

    v0.7.0 (December 13, 2018)

    • Test that MOI.TerminationStatus is MOI.OptimizeNotCalled before MOI.optimize! is called.
    • Check supports_default_copy_to in tests (#594).
    • Key pieces of information like optimality, infeasibility, etc., are now reported through TerminationStatusCode. It is typically no longer necessary to check the result statuses in addition to the termination status.
    • Add perspective dimension to log-det cone (#593).

    v0.6.4 (November 27, 2018)

    • Add OptimizeNotCalled termination status (#577) and improve documentation of other statuses (#575).
    • Add a solver naming guideline (#578).
    • Make FeasibilitySense the default ObjectiveSense (#579).
    • Fix Utilities.@model and Bridges.@bridge macros for functions and sets defined outside MOI (#582).
    • Document solver-specific attributes (#580) and implement them in Utilities.CachingOptimizer (#565).

    v0.6.3 (November 16, 2018)

    • Variables and constraints are now allowed to have duplicate names. An error is thrown only on lookup. This change breaks some existing tests. (#549)
    • Attributes may now be partially set (some values could be nothing). (#563)
    • Performance improvements in Utilities.Model (#549, #567, #568)
    • Fix bug in QuadtoSOC (#558).
    • New supports_default_copy_to method that optimizers should implement to control caching behavior.
    • Documentation improvements.

    v0.6.2 (October 26, 2018)

    • Improve hygiene of @model macro (#544).
    • Fix bug in copy tests (#543).
    • Fix bug in UniversalFallback attribute getter (#540).
    • Allow all correct solutions for solve_blank_obj unit test (#537).
    • Add errors for Allocate-Load and bad constraints (#534).
    • [performance] Add specialized implementation of hash for VariableIndex (#533).
    • [performance] Construct the name to object dictionaries lazily in model (#535).
    • Add the QuadtoSOC bridge which transforms ScalarQuadraticFunction constraints into RotatedSecondOrderCone (#483).

    v0.6.1 (September 22, 2018)

    • Enable PositiveSemidefiniteConeSquare set and quadratic functions in MOIB.fullbridgeoptimizer (#524).
    • Add warning in the bridge between PositiveSemidefiniteConeSquare and PositiveSemidefiniteConeTriangle when the matrix is almost symmetric (#522).
    • Modify MOIT.copytest to not add multiples constraints on the same variable (#521).
    • Add missing keyword argument in one of MOIU.add_scalar_constraint methods (#520).

    v0.6.0 (August 30, 2018)

    • The MOIU.@model and MOIB.@bridge macros now support functions and sets defined in external modules. As a consequence, function and set names in the macro arguments need to be prefixed by module name.
    • Rename functions according to the JuMP style guide:
      • copy! with keyword arguments copynames and warnattributes -> copy_to with keyword arguments copy_names and warn_attributes;
      • set! -> set;
      • addvariable[s]! -> add_variable[s];
      • supportsconstraint -> supports_constraint;
      • addconstraint[s]! -> add_constraint[s];
      • isvalid -> is_valid;
      • isempty -> is_empty;
      • Base.delete! -> delete;
      • modify! -> modify;
      • transform! -> transform;
      • initialize! -> initialize;
      • write -> write_to_file; and
      • read! -> read_from_file.
    • Remove free! (use Base.finalize instead).
    • Add the SquarePSD bridge which transforms PositiveSemidefiniteConeTriangle constraints into PositiveSemidefiniteConeTriangle.
    • Add result fallback for ConstraintDual of variable-wise constraint, ConstraintPrimal and ObjectiveValue.
    • Add tests for ObjectiveBound.
    • Add test for empty rows in vector linear constraint.
    • Rework errors: CannotError has been renamed NotAllowedError and the distinction between UnsupportedError and NotAllowedError is now about whether the element is not supported (for example, it cannot be copied a model containing this element) or the operation is not allowed (either because it is not implemented, because it cannot be performed in the current state of the model, or because it cannot be performed for a specific index)
    • canget is removed. NoSolution is added as a result status to indicate that the solver does not have either a primal or dual solution available (See #479).

    v0.5.0 (August 5, 2018)

    • Fix names with CachingOptimizer.
    • Cleanup thanks to @mohamed82008.
    • Added a universal fallback for constraints.
    • Fast utilities for function canonicalization thanks to @rdeits.
    • Renamed dimension field to side_dimension in the context of matrix-like sets.
    • New and improved tests for cases like duplicate terms and ObjectiveBound.
    • Removed cantransform, canaddconstraint, canaddvariable, canset, canmodify, and candelete functions from the API. They are replaced by a new set of errors that are thrown: Subtypes of UnsupportedError indicate unsupported operations, while subtypes of CannotError indicate operations that cannot be performed in the current state.
    • The API for copy! is updated to remove the CopyResult type.
    • Updates for the new JuMP style guide.

    v0.4.1 (June 28, 2018)

    • Fixes vector function modification on 32 bits.
    • Fixes Bellman-Ford algorithm for bridges.
    • Added an NLP test with FeasibilitySense.
    • Update modification documentation.

    v0.4.0 (June 23, 2018)

    • Helper constructors for VectorAffineTerm and VectorQuadraticTerm.
    • Added modify_lhs to TestConfig.
    • Additional unit tests for optimizers.
    • Added a type parameter to CachingOptimizer for the optimizer field.
    • New API for problem modification (#388)
    • Tests pass without deprecation warnings on Julia 0.7.
    • Small fixes and documentation updates.

    v0.3.0 (May 25, 2018)

    • Functions have been redefined to use arrays-of-structs instead of structs-of-arrays.
    • Improvements to MockOptimizer.
    • Significant changes to Bridges.
    • New and improved unit tests.
    • Fixes for Julia 0.7.

    v0.2.0 (April 24, 2018)

    • Improvements to and better coverage of Tests.
    • Documentation fixes.
    • SolverName attribute.
    • Changes to the NLP interface (new definition of variable order and arrays of structs for bound pairs and sparsity patterns).
    • Addition of NLP tests.
    • Introduction of UniversalFallback.
    • copynames keyword argument to MOI.copy!.
    • Add Bridges submodule.

    v0.1.0 (February 28, 2018)

    • Initial public release.
    • The framework for MOI was developed at the JuMP-dev workshop at MIT in June 2017 as a sorely needed replacement for MathProgBase.
    +end

    v0.9.22 (May 22, 2021)

    This release contains backports from the ongoing development of the v0.10 release.

    • Improved type inference in Utilities, Bridges and FileFormats submodules to reduce latency.
    • Improved performance of Utilities.is_canonical.
    • Fixed Utilities.pass_nonvariable_constraints with bridged variables.
    • Fixed performance regression of Utilities.Model.
    • Fixed ordering of objective setting in parser.

    v0.9.21 (April 23, 2021)

    • Added supports_shift_constant.
    • Improve performance of bridging quadratic constraints.
    • Add precompilation statements.
    • Large improvements to the documentation.
    • Fix a variety of inference issues, benefiting precompilation and reducing initial latency.
    • RawParameters are now ignored when resetting a CachingOptimizer. Previously, changing the underlying optimizer after RawParameters were set would throw an error.
    • Utilities.AbstractModel is being refactored. This may break users interacting with private fields of a model generated using @model.

    v0.9.20 (February 20, 2021)

    • Improved performance of Utilities.ScalarFunctionIterator
    • Added support for compute_conflict to MOI layers
    • Added test with zero off-diagonal quadratic term in objective
    • Fixed double deletion of nested bridged SingleVariable/VectorOfVariables constraints
    • Fixed modification of un-set objective
    • Fixed function modification with duplicate terms
    • Made unit tests abort without failing if the problem class is not supported
    • Formatted code with JuliaFormatter
    • Clarified BasisStatusCode's docstring

    v0.9.19 (December 1, 2020)

    • Added CallbackNodeStatus attribute
    • Added bridge from GreaterThan or LessThan to Interval
    • Added tests for infeasibility certificates and double optimize
    • Fixed support for Julia v1.6
    • Re-organized MOI docs and added documentation for adding a test

    v0.9.18 (November 3, 2020)

    • Various improvements for working with complex numbers
    • Added GeoMeantoRelEntrBridge to bridge a GeometricMeanCone constraint to a relative entropy constraint

    v0.9.17 (September 21, 2020)

    • Fixed CleverDict with variable of negative index value
    • Implement supports_add_constrained_variable for MockOptimizer

    v0.9.16 (September 17, 2020)

    • Various fixes:
      • 32-bit support
      • CleverDict with abstract value type
      • Checks in test suite

    v0.9.15 (September 14, 2020)

    • Bridges improvements:
      • (R)SOCtoNonConvexQuad bridge
      • ZeroOne bridge
      • Use supports_add_constrained_variable in LazyBridgeOptimizer
      • Exposed VariableBridgeCost and ConstraintBridgeCost attributes
      • Prioritize constraining variables on creation according to these costs
      • Refactor bridge debugging
    • Large performance improvements across all submodules
    • Lots of documentation improvements
    • FileFormats improvements:
      • Update MathOptFormat to v0.5
      • Fix supported objectives in FileFormats
    • Testing improvements:
      • Add name option for basic_constraint_test
    • Bug fixes and missing methods
      • Add length for iterators
      • Fix bug with duplicate terms
      • Fix order of LinearOfConstraintIndices

    v0.9.14 (May 30, 2020)

    • Add a solver-independent interface for accessing the set of conflicting constraints an Irreducible Inconsistent Subsystem (#1056).
    • Bump JSONSchema dependency from v0.2 to v0.3 (#1090).
    • Documentation improvements:
      • Fix typos (#1054, #1060, #1061, #1064, #1069, #1070).
      • Remove the outdated recommendation for a package implementing MOI for a solver XXX to be called MathOptInterfaceXXX (#1087).
    • Utilities improvements:
      • Fix is_canonical for quadratic functions (#1081, #1089).
      • Implement add_constrained_variable[s] for CachingOptimizer so that it is added as constrained variables to the underlying optimizer (#1084).
      • Add support for custom objective functions for UniversalFallback (#1086).
      • Deterministic ordering of constraints in UniversalFallback (#1088).
    • Testing improvements:
      • Add NormOneCone/NormInfinityCone tests (#1045).
    • Bridges improvements:
      • Add bridges from Semiinteger and Semicontinuous (#1059).
      • Implement getting ConstraintSet for Variable.FlipSignBridge (#1066).
      • Fix setting ConstraintFunction for Constraint.ScalarizeBridge (#1093).
      • Fix NormOne/NormInf bridges with nonzero constants (#1045).
      • Fix StackOverflow in debug (#1063).
    • FileFormats improvements:
      • [SDPA] Implement the extension for integer variables (#1079).
      • [SDPA] Ignore comments after m and nblocks and detect dat-s extension (#1077).
      • [SDPA] No scaling of off-diagonal coefficient (#1076).
      • [SDPA] Add missing negation of constant (#1075).

    v0.9.13 (March 24, 2020)

    • Added tests for Semicontinuous and Semiinteger variables (#1033).
    • Added tests for using ExprGraphs from NLP evaluators (#1043).
    • Update version compatibilities of dependencies (#1034, #1051, #1052).
    • Fixed typos in documentation (#1044).

    v0.9.12 (February 28, 2020)

    • Fixed writing NLPBlock in MathOptFormat (#1037).
    • Fixed MockOptimizer for result attributes with non-one result index (#1039).
    • Updated test template with instantiate (#1032).

    v0.9.11 (February 21, 2020)

    • Add an option for the model created by Utilities.@model to be a subtype of AbstractOptimizer (#1031).
    • Described dual cone in docstrings of GeoMeanCone and RelativeEntropyCone (#1018, #1028).
    • Fixed typos in documentation (#1022, #1024).
    • Fixed warning of unsupported attribute (#1027).
    • Added more rootdet/logdet conic tests (#1026).
    • Implemented ConstraintDual for Constraint.GeoMeanBridge, Constraint.RootDetBridge and Constraint.LogDetBridge and test duals in tests with GeoMeanCone and RootDetConeTriangle and LogDetConeTriangle cones (#1025, #1026).

    v0.9.10 (January 31, 2020)

    • Added OptimizerWithAttributes grouping an optimizer constructor and a list of optimizer attributes (#1008).
    • Added RelativeEntropyCone with corresponding bridge into exponential cone constraints (#993).
    • Added NormSpectralCone and NormNuclearCone with corresponding bridges into positive semidefinite constraints (#976).
    • Added supports_constrained_variable(s) (#1004).
    • Added dual_set_type (#1002).
    • Added tests for vector specialized version of delete (#989, #1011).
    • Added PSD3 test (#1007).
    • Clarified dual solution of Tests.pow1v and Tests.pow1f (#1013).
    • Added support for EqualTo and Zero in Bridges.Constraint.SplitIntervalBridge (#1005).
    • Fixed Utilities.vectorize for empty vector (#1003).
    • Fixed free variables in LP writer (#1006).

    v0.9.9 (December 29, 2019)

    • Incorporated MathOptFormat.jl as the FileFormats submodule. FileFormats provides readers and writers for a number of standard file formats and MOF, a file format specialized for MOI (#969).
    • Improved performance of deletion of vector of variables in MOI.Utilities.Model (#983).
    • Updated to MutableArithmetics v0.2 (#981).
    • Added MutableArithmetics.promote_operation allocation tests (#975).
    • Fixed inference issue on Julia v1.1 (#982).

    v0.9.8 (December 19, 2019)

    • Implemented MutableArithmetics API (#924).
    • Fixed callbacks with CachingOptimizer (#959).
    • Fixed MOI.dimension for MOI.Complements (#948).
    • Added fallback for add_variables (#972).
    • Added is_diagonal_vectorized_index utility (#965).
    • Improved linear constraints display in manual (#963, #964).
    • Bridges improvements:
      • Added IndicatorSet to SOS1 bridge (#877).
      • Added support for starting values for Variable.VectorizeBridge (#944).
      • Fixed MOI.add_constraints with non-bridged variable constraint on bridged variable (#951).
      • Fixed corner cases and docstring of GeoMeanBridge (#961, #962, #966).
      • Fixed choice between variable or constraint bridges for constrained variables (#973).
      • Improve performance of bridge shortest path (#945, #946, #956).
      • Added docstring for test_delete_bridge (#954).
      • Added Variable bridge tests (#952).

    v0.9.7 (October 30, 2019)

    • Implemented _result_index_field for NLPBlockDual (#934).
    • Fixed copy of model with starting values for vector constraints (#941).
    • Bridges improvements:
      • Improved performance of add_bridge and added has_bridge (#935).
      • Added AbstractSetMapBridge for bridges between sets S1, S2 such that there is a linear map A such that A*S1 = S2 (#933).
      • Added support for starting values for FlipSignBridge, VectorizeBridge, ScalarizeBridge, SlackBridge, SplitIntervalBridge, RSOCBridge, SOCRBridge NormInfinityBridge, SOCtoPSDBridge and RSOCtoPSDBridge (#933, #936, #937, #938, #939).

    v0.9.6 (October 25, 2019)

    • Added complementarity constraints (#913).
    • Allowed ModelLike objects as value of attributes (#928).
    • Testing improvements:
      • Added dual_objective_value option to MOI.Test.TestConfig (#922).
      • Added InvalidIndex tests in basic_constraint_tests (#921).
      • Added tests for the constant term in indicator constraint (#929).
    • Bridges improvements:
      • Added support for starting values for Functionize bridges (#923).
      • Added variable indices context to variable bridges (#920).
      • Fixed a typo in printing o debug_supports (#927).

    v0.9.5 (October 9, 2019)

    • Clarified PrimalStatus/DualStatus to be NO_SOLUTION if result_index is out of bounds (#912).
    • Added tolerance for checks and use ResultCount + 1 for the result_index in MOI.Test.solve_result_status (#910, #917).
    • Use 0.5 instead of 2.0 for power in PowerCone in basic_constraint_test (#916).
    • Bridges improvements:
      • Added debug utilities for unsupported variable/constraint/objective (#861).
      • Fixed deletion of variables in bridged VectorOfVariables constraints (#909).
      • Fixed result_index with objective bridges (#911).

    v0.9.4 (October 2, 2019)

    • Added solver-independent MIP callbacks (#782).
    • Implements submit for Utilities.CachingOptimizer and Bridges.AbstractBridgeOptimizer (#906).
    • Added tests for result count of solution attributes (#901, #904).
    • Added NumberOfThreads attribute (#892).
    • Added Utilities.get_bounds to get the bounds on a variable (#890).
    • Added a note on duplicate coefficients in documentation (#581).
    • Added result index in ConstraintBasisStatus (#898).
    • Added extension dictionary to Utilities.Model (#884, #895).
    • Fixed deletion of constrained variables for CachingOptimizer (#905).
    • Implemented Utilities.shift_constraint for Test.UnknownScalarSet (#896).
    • Bridges improvements:
      • Added Variable.RSOCtoSOCBridge (#907).
      • Implemented MOI.get for ConstraintFunction/ConstraintSet for Bridges.Constraint.SquareBridge (#899).

    v0.9.3 (September 20, 2019)

    • Fixed ambiguity detected in Julia v1.3 (#891, #893).
    • Fixed missing sets from ListOfSupportedConstraints (#880).
    • Fixed copy of VectorOfVariables constraints with duplicate indices (#886).
    • Added extension dictionary to MOIU.Model (#884).
    • Implemented MOI.get for function and set for GeoMeanBridge (#888).
    • Updated documentation for SingleVariable indices and bridges (#885).
    • Testing improvements:
      • Added more comprehensive tests for names (#882).
      • Added tests for SingleVariable duals (#883).
      • Added tests for DualExponentialCone and DualPowerCone (#873).
    • Improvements for arbitrary coefficient type:
      • Fixed == for sets with mutable fields (#887).
      • Removed some Float64 assumptions in bridges (#878).
      • Automatic selection of Constraint.[Scalar|Vector]FunctionizeBridge (#889).

    v0.9.2 (September 5, 2019)

    • Implemented model printing for MOI.ModelLike and specialized it for models defined in MOI (864).
    • Generalized contlinear tests for arbitrary coefficient type (#855).
    • Fixed supports_constraint for Semiinteger and Semicontinuous and supports for ObjectiveFunction (#859).
    • Fixed Allocate-Load copy for single variable constraints (#856).
    • Bridges improvements:
      • Add objective bridges (#789).
      • Fixed Variable.RSOCtoPSDBridge for dimension 2 (#869).
      • Added Variable.SOCtoRSOCBridge (#865).
      • Added Constraint.SOCRBridge and disable MOI.Bridges.Constraint.SOCtoPSDBridge (#751).
      • Fixed added_constraint_types for Contraint.LogDetBridge and Constraint.RootDetBridge (#870).

    v0.9.1 (August 22, 2019)

    • Fix support for Julia v1.2 (#834).
    • L1 and L∞ norm epigraph cones and corresponding bridges to LP were added (#818).
    • Added tests to MOI.Test.nametest (#833).
    • Fix MOI.Test.soc3test for solvers not supporting infeasibility certificates (#839).
    • Implements operate for operators * and / between vector function and constant (#837).
    • Implements show for MOI.Utilities.IndexMap (#847).
    • Fix corner cases for mapping of variables in MOI.Utilities.CachingOptimizer and substitution of variables in MOI.Bridges.AbstractBridgeOptimizer (#848).
    • Fix transformation of constant terms for MOI.Bridges.Constraint.SOCtoPSDBridge and MOI.Bridges.Constraint.RSOCtoPSDBridge (#840).

    v0.9.0 (August 13, 2019)

    • Support for Julia v0.6 and v0.7 was dropped (#714, #717).
    • A MOI.Utilities.Model implementation of ModelLike, this should replace most use cases of MOI.Utilities.@model (#781).
    • add_constrained_variable and add_constrained_variables were added (#759).
    • Support for indicator constraints was added (#709, #712).
    • DualObjectiveValue attribute was added (#473).
    • RawParameter attribute was added (#733).
    • A dual_set function was added (#804).
    • A Benchmarks submodule was added to facilitate solver benchmarking (#769).
    • A submit function was added, this may for instance allow the user to submit solutions or cuts to the solver from a callback (#775).
    • The field of ObjectiveValue was renamed to result_index (#729).
    • The _constant and Utilities.getconstant function were renamed to constant
    • REDUCTION_CERTIFICATE result status was added (#734).
    • Abstract matrix sets were added (#731).
    • Testing improvements:
      • The testing guideline was updated (#728).
      • Quadratic tests were added (#697).
      • Unit tests for RawStatusString, SolveTime, Silent and SolverName were added (#726, #741).
      • A rotated second-order cone test was added (#759).
      • A power cone test was added (#768).
      • Tests for ZeroOne variables with variable bounds were added (#772).
      • An unbounded test was added (#773).
      • Existing tests had a few updates (#702, #703, #763).
    • Documentation improvements:
      • Added a section on CachingOptimizer (#777).
      • Added a section on UniversalFallback, Model and @model (#762).
      • Transition the knapsack example to a doctest with MockOptimizer (#786).
    • Utilities improvements:
      • A CleverDict utility was added for a vector that automatically transform into a dictionary once a first index is removed (#767).
      • The Utilities.constant function was renamed to Utilities.constant_vector (#740).
      • Implement optimizer attributes for CachingOptimizer (#745).
      • Rename Utilities.add_scalar_constraint to Utilities.normalize_and_add_constraint (#801).
      • operate with vcat, SingleVariable and VectorOfVariables now returns a VectorOfVariables (#616).
      • Fix a type piracy of operate (#784).
      • The load_constraint fallback signature was fixed (#760).
      • The set_dot function was extended to work with sparse arrays (#805).
    • Bridges improvements:
      • The bridges no longer store the constraint function and set before it is bridged, the bridges now have to implement ConstraintFunction and ConstraintSet if the user wants to recover them. As a consequence, the @bridge macro was removed (#722).
      • Bridge are now instantiated with a bridge_constraint function instead of using a constructor (#730).
      • Fix constraint attributes for bridges (#699).
      • Constraint bridges were moved to the Bridges/Constraint submodule so they should now inherit from MOI.Bridges.Constraint.Abstract and should implement MOI.Bridges.Constraint.concrete_bridge_type instead of MOI.Bridges.concrete_bridge_type (#756).
      • Variable bridges were added in (#759).
      • Various improvements (#746, #747).

    v0.8.4 (March 13, 2019)

    • Performance improvement in default_copy_to and bridge optimizer (#696).
    • Add Silent and implement setting optimizer attributes in caching and mock optimizers (#695).
    • Add Functionize bridges (SingleVariable and VectorOfVariables) (#659).
    • Minor typo fixes (#694).

    v0.8.3 (March 6, 2019)

    • Use zero constant in scalar constraint function of MOI.Test.copytest (#691).
    • Fix variable deletion with SingleVariable objective function (#690).
    • Fix LazyBridgeOptimizer with bridges that add no constraints (#689).
    • Error message improvements (#673, #685, #686, #688).
    • Documentation improvements (#682, #683, #687).
    • Basis status:
      • Remove VariableBasisStatus (#679).
      • Test ConstraintBasisStatus and implement it in bridges (#678).
    • Fix inference of NumberOfVariables and NumberOfConstraints (#677).
    • Implement division between a quadratic function and a number (#675).

    v0.8.2 (February 7, 2019)

    • Add RawStatusString attribute (#629).
    • Do not set names to the optimizer but only to the cache in CachingOptimizer (#638).
    • Make scalar MOI functions act as scalars in broadcast (#646).
    • Add function utilities:
      • Implement Base.zero (#634), Base.iszero (#643), add missing arithmetic operations (#644, #645) and fix division (#648).
      • Add a vectorize function that turns a vector of ScalarAffineFunction into a VectorAffineFunction (#642).
    • Improve support for starting values:
      • Show a warning in copy when starting values are not supported instead of throwing an error (#630).
      • Fix UniversalFallback for getting an variable or constraint attribute set to no indices (#623).
      • Add a test in contlineartest with partially set VariablePrimalStart.
    • Bridges improvements:
      • Fix StackOverFlow in LazyBridgeOptimizer when there is a cycle in the graph of bridges.
      • Add Slack bridges (#610, #650).
      • Add FlipSign bridges (#658).
    • Add tests with duplicate coefficients in ScalarAffineFunction and VectorAffineFunction (#639).
    • Use tolerance to compare VariablePrimal in rotatedsoc1 test (#632).
    • Use a zero constant in ScalarAffineFunction of constraints in psdt2 (#622).

    v0.8.1 (January 7, 2019)

    • Adding an NLP objective now overrides any objective set using the ObjectiveFunction attribute (#619).
    • Rename fullbridgeoptimizer into full_bridge_optimizer (#621).
    • Allow custom constraint types with full_bridge_optimizer (#617).
    • Add Vectorize bridge which transforms scalar linear constraints into vector linear constraints (#615).

    v0.8.0 (December 18, 2018)

    • Rename all enum values to follow the JuMP naming guidelines for constants, for example, Optimal becomes OPTIMAL, and DualInfeasible becomes DUAL_INFEASIBLE.
    • Rename CachingOptimizer methods for style compliance.
    • Add an MOI.TerminationStatusCode called ALMOST_DUAL_INFEASIBLE.

    v0.7.0 (December 13, 2018)

    • Test that MOI.TerminationStatus is MOI.OptimizeNotCalled before MOI.optimize! is called.
    • Check supports_default_copy_to in tests (#594).
    • Key pieces of information like optimality, infeasibility, etc., are now reported through TerminationStatusCode. It is typically no longer necessary to check the result statuses in addition to the termination status.
    • Add perspective dimension to log-det cone (#593).

    v0.6.4 (November 27, 2018)

    • Add OptimizeNotCalled termination status (#577) and improve documentation of other statuses (#575).
    • Add a solver naming guideline (#578).
    • Make FeasibilitySense the default ObjectiveSense (#579).
    • Fix Utilities.@model and Bridges.@bridge macros for functions and sets defined outside MOI (#582).
    • Document solver-specific attributes (#580) and implement them in Utilities.CachingOptimizer (#565).

    v0.6.3 (November 16, 2018)

    • Variables and constraints are now allowed to have duplicate names. An error is thrown only on lookup. This change breaks some existing tests. (#549)
    • Attributes may now be partially set (some values could be nothing). (#563)
    • Performance improvements in Utilities.Model (#549, #567, #568)
    • Fix bug in QuadtoSOC (#558).
    • New supports_default_copy_to method that optimizers should implement to control caching behavior.
    • Documentation improvements.

    v0.6.2 (October 26, 2018)

    • Improve hygiene of @model macro (#544).
    • Fix bug in copy tests (#543).
    • Fix bug in UniversalFallback attribute getter (#540).
    • Allow all correct solutions for solve_blank_obj unit test (#537).
    • Add errors for Allocate-Load and bad constraints (#534).
    • [performance] Add specialized implementation of hash for VariableIndex (#533).
    • [performance] Construct the name to object dictionaries lazily in model (#535).
    • Add the QuadtoSOC bridge which transforms ScalarQuadraticFunction constraints into RotatedSecondOrderCone (#483).

    v0.6.1 (September 22, 2018)

    • Enable PositiveSemidefiniteConeSquare set and quadratic functions in MOIB.fullbridgeoptimizer (#524).
    • Add warning in the bridge between PositiveSemidefiniteConeSquare and PositiveSemidefiniteConeTriangle when the matrix is almost symmetric (#522).
    • Modify MOIT.copytest to not add multiples constraints on the same variable (#521).
    • Add missing keyword argument in one of MOIU.add_scalar_constraint methods (#520).

    v0.6.0 (August 30, 2018)

    • The MOIU.@model and MOIB.@bridge macros now support functions and sets defined in external modules. As a consequence, function and set names in the macro arguments need to be prefixed by module name.
    • Rename functions according to the JuMP style guide:
      • copy! with keyword arguments copynames and warnattributes -> copy_to with keyword arguments copy_names and warn_attributes;
      • set! -> set;
      • addvariable[s]! -> add_variable[s];
      • supportsconstraint -> supports_constraint;
      • addconstraint[s]! -> add_constraint[s];
      • isvalid -> is_valid;
      • isempty -> is_empty;
      • Base.delete! -> delete;
      • modify! -> modify;
      • transform! -> transform;
      • initialize! -> initialize;
      • write -> write_to_file; and
      • read! -> read_from_file.
    • Remove free! (use Base.finalize instead).
    • Add the SquarePSD bridge which transforms PositiveSemidefiniteConeTriangle constraints into PositiveSemidefiniteConeTriangle.
    • Add result fallback for ConstraintDual of variable-wise constraint, ConstraintPrimal and ObjectiveValue.
    • Add tests for ObjectiveBound.
    • Add test for empty rows in vector linear constraint.
    • Rework errors: CannotError has been renamed NotAllowedError and the distinction between UnsupportedError and NotAllowedError is now about whether the element is not supported (for example, it cannot be copied a model containing this element) or the operation is not allowed (either because it is not implemented, because it cannot be performed in the current state of the model, or because it cannot be performed for a specific index)
    • canget is removed. NoSolution is added as a result status to indicate that the solver does not have either a primal or dual solution available (See #479).

    v0.5.0 (August 5, 2018)

    • Fix names with CachingOptimizer.
    • Cleanup thanks to @mohamed82008.
    • Added a universal fallback for constraints.
    • Fast utilities for function canonicalization thanks to @rdeits.
    • Renamed dimension field to side_dimension in the context of matrix-like sets.
    • New and improved tests for cases like duplicate terms and ObjectiveBound.
    • Removed cantransform, canaddconstraint, canaddvariable, canset, canmodify, and candelete functions from the API. They are replaced by a new set of errors that are thrown: Subtypes of UnsupportedError indicate unsupported operations, while subtypes of CannotError indicate operations that cannot be performed in the current state.
    • The API for copy! is updated to remove the CopyResult type.
    • Updates for the new JuMP style guide.

    v0.4.1 (June 28, 2018)

    • Fixes vector function modification on 32 bits.
    • Fixes Bellman-Ford algorithm for bridges.
    • Added an NLP test with FeasibilitySense.
    • Update modification documentation.

    v0.4.0 (June 23, 2018)

    • Helper constructors for VectorAffineTerm and VectorQuadraticTerm.
    • Added modify_lhs to TestConfig.
    • Additional unit tests for optimizers.
    • Added a type parameter to CachingOptimizer for the optimizer field.
    • New API for problem modification (#388)
    • Tests pass without deprecation warnings on Julia 0.7.
    • Small fixes and documentation updates.

    v0.3.0 (May 25, 2018)

    • Functions have been redefined to use arrays-of-structs instead of structs-of-arrays.
    • Improvements to MockOptimizer.
    • Significant changes to Bridges.
    • New and improved unit tests.
    • Fixes for Julia 0.7.

    v0.2.0 (April 24, 2018)

    • Improvements to and better coverage of Tests.
    • Documentation fixes.
    • SolverName attribute.
    • Changes to the NLP interface (new definition of variable order and arrays of structs for bound pairs and sparsity patterns).
    • Addition of NLP tests.
    • Introduction of UniversalFallback.
    • copynames keyword argument to MOI.copy!.
    • Add Bridges submodule.

    v0.1.0 (February 28, 2018)

    • Initial public release.
    • The framework for MOI was developed at the JuMP-dev workshop at MIT in June 2017 as a sorely needed replacement for MathProgBase.
    diff --git a/previews/PR3913/moi/submodules/Benchmarks/overview/index.html b/previews/PR3913/moi/submodules/Benchmarks/overview/index.html index 9a8e21f15c6..ad75322370e 100644 --- a/previews/PR3913/moi/submodules/Benchmarks/overview/index.html +++ b/previews/PR3913/moi/submodules/Benchmarks/overview/index.html @@ -21,4 +21,4 @@ MOI.Benchmarks.compare_against_baseline( suite, "current"; directory = "/tmp", verbose = true -)

    This comparison will create a report detailing improvements and regressions.

    +)

    This comparison will create a report detailing improvements and regressions.

    diff --git a/previews/PR3913/moi/submodules/Benchmarks/reference/index.html b/previews/PR3913/moi/submodules/Benchmarks/reference/index.html index 4354b456091..557fefc0107 100644 --- a/previews/PR3913/moi/submodules/Benchmarks/reference/index.html +++ b/previews/PR3913/moi/submodules/Benchmarks/reference/index.html @@ -37,4 +37,4 @@ "glpk_master"; directory = "/tmp", verbose = true, - )source + )source diff --git a/previews/PR3913/moi/submodules/Bridges/implementation/index.html b/previews/PR3913/moi/submodules/Bridges/implementation/index.html index b0d1b2d07db..7bf5460421f 100644 --- a/previews/PR3913/moi/submodules/Bridges/implementation/index.html +++ b/previews/PR3913/moi/submodules/Bridges/implementation/index.html @@ -33,4 +33,4 @@ Subject to: ScalarAffineFunction{Int64}-in-LessThan{Int64} - (0) - (1) x <= (-1) + (0) - (1) x <= (-1) diff --git a/previews/PR3913/moi/submodules/Bridges/list_of_bridges/index.html b/previews/PR3913/moi/submodules/Bridges/list_of_bridges/index.html index f38724d5a9a..109418bbff9 100644 --- a/previews/PR3913/moi/submodules/Bridges/list_of_bridges/index.html +++ b/previews/PR3913/moi/submodules/Bridges/list_of_bridges/index.html @@ -129,4 +129,4 @@ & & & x_{11} & x_{12} & x_{13} \\ & & & & x_{22} & x_{23} \\ & & & & & x_{33} -\end{bmatrix}\]

    is positive semidefinite.

    The bridge achieves this reformulation by adding a new set of variables in MOI.PositiveSemidefiniteConeTriangle(6), and then adding three groups of equality constraints to:

    • constrain the two x blocks to be equal
    • force the diagonal of the y blocks to be 0
    • force the lower triangular of the y block to be the negative of the upper triangle.
    source
    MathOptInterface.Bridges.Variable.RSOCtoPSDBridge — Type
    RSOCtoPSDBridge{T} <: Bridges.Variable.AbstractBridge

    RSOCtoPSDBridge implements the following reformulation:

    • $||x||_2^2 \le 2tu$ where $t, u \ge 0$ into $Y \succeq 0$, with the substitution rule: $Y = \left[\begin{array}{c c}t & x^\top \\ x & 2u \mathbf{I}\end{array}\right].$

    Additional bounds are added to ensure the off-diagonals of the $2uI$ submatrix are 0, and linear constraints are added to ensure the diagonal of $2uI$ takes the same values.

    As a special case, if $|x|| = 0$, then RSOCtoPSDBridge reformulates into $(t, u) \in \mathbb{R}_+$.

    Source node

    RSOCtoPSDBridge supports:

    Target nodes

    RSOCtoPSDBridge creates:

    source
    MathOptInterface.Bridges.Variable.RSOCtoSOCBridge — Type
    RSOCtoSOCBridge{T} <: Bridges.Variable.AbstractBridge

    RSOCtoSOCBridge implements the following reformulation:

    • $||x||_2^2 \le 2tu$ into $||v||_2 \le w$, with the substitution rules $t = \frac{w}{\sqrt 2} + \frac{v_1}{\sqrt 2}$, $u = \frac{w}{\sqrt 2} - \frac{v_1}{\sqrt 2}$, and $x = (v_2,\ldots,v_N)$.

    Source node

    RSOCtoSOCBridge supports:

    Target node

    RSOCtoSOCBridge creates:

    source
    MathOptInterface.Bridges.Variable.SOCtoRSOCBridge — Type
    SOCtoRSOCBridge{T} <: Bridges.Variable.AbstractBridge

    SOCtoRSOCBridge implements the following reformulation:

    • $||x||_2 \le t$ into $2uv \ge ||w||_2^2$, with the substitution rules $t = \frac{u}{\sqrt 2} + \frac{v}{\sqrt 2}$, $x = (\frac{u}{\sqrt 2} - \frac{v}{\sqrt 2}, w)$.

    Assumptions

    • SOCtoRSOCBridge assumes that $|x| \ge 1$.

    Source node

    SOCtoRSOCBridge supports:

    Target node

    SOCtoRSOCBridge creates:

    source
    MathOptInterface.Bridges.Variable.SetMapBridge — Type
    abstract type SetMapBridge{T,S1,S2} <: AbstractBridge end

    Consider two type of sets, S1 and S2, and a linear mapping A such that the image of a set of type S1 under A is a set of type S2.

    A SetMapBridge{T,S1,S2} is a bridge that substitutes constrained variables in S2 into the image through A of constrained variables in S1.

    The linear map A is described by:

    Implementing a method for these two functions is sufficient to bridge constrained variables. However, in order for the getters and setters of attributes such as dual solutions and starting values to work as well, a method for the following functions must be implemented:

    See the docstrings of each function to see which feature would be missing if it was not implemented for a given bridge.

    source
    MathOptInterface.Bridges.Variable.VectorizeBridge — Type
    VectorizeBridge{T,S} <: Bridges.Variable.AbstractBridge

    VectorizeBridge implements the following reformulations:

    • $x \ge a$ into $[y] \in \mathbb{R}_+$ with the substitution rule $x = a + y$
    • $x \le a$ into $[y] \in \mathbb{R}_-$ with the substitution rule $x = a + y$
    • $x == a$ into $[y] \in \{0\}$ with the substitution rule $x = a + y$

    where T is the coefficient type of a + y.

    Source node

    VectorizeBridge supports:

    Target nodes

    VectorizeBridge creates:

    source
    MathOptInterface.Bridges.Variable.ZerosBridge — Type
    ZerosBridge{T} <: Bridges.Variable.AbstractBridge

    ZerosBridge implements the following reformulation:

    • $x \in \{0\}$ into the substitution rule $x = 0$,

    where T is the coefficient type of 0.

    Source node

    ZerosBridge supports:

    Target nodes

    ZerosBridge does not create target nodes. It replaces all instances of x with 0 via substitution. This means that no variables are created in the underlying model.

    Caveats

    The bridged variables are similar to parameters with zero values. Parameters with non-zero values can be created with constrained variables in MOI.EqualTo by combining a VectorizeBridge and this bridge.

    However, functions modified by ZerosBridge cannot be unbridged. That is, for a given function, we cannot determine if the bridged variables were used.

    A related implication is that this bridge does not support MOI.ConstraintDual. However, if a MOI.Utilities.CachingOptimizer is used, the dual can be determined by the bridged optimizer using MOI.Utilities.get_fallback because the caching optimizer records the unbridged function.

    source
    +\end{bmatrix}\]

    is positive semidefinite.

    The bridge achieves this reformulation by adding a new set of variables in MOI.PositiveSemidefiniteConeTriangle(6), and then adding three groups of equality constraints to:

    • constrain the two x blocks to be equal
    • force the diagonal of the y blocks to be 0
    • force the lower triangular of the y block to be the negative of the upper triangle.
    source
    MathOptInterface.Bridges.Variable.RSOCtoPSDBridge — Type
    RSOCtoPSDBridge{T} <: Bridges.Variable.AbstractBridge

    RSOCtoPSDBridge implements the following reformulation:

    • $||x||_2^2 \le 2tu$ where $t, u \ge 0$ into $Y \succeq 0$, with the substitution rule: $Y = \left[\begin{array}{c c}t & x^\top \\ x & 2u \mathbf{I}\end{array}\right].$

    Additional bounds are added to ensure the off-diagonals of the $2uI$ submatrix are 0, and linear constraints are added to ensure the diagonal of $2uI$ takes the same values.

    As a special case, if $|x|| = 0$, then RSOCtoPSDBridge reformulates into $(t, u) \in \mathbb{R}_+$.

    Source node

    RSOCtoPSDBridge supports:

    Target nodes

    RSOCtoPSDBridge creates:

    source
    MathOptInterface.Bridges.Variable.RSOCtoSOCBridge — Type
    RSOCtoSOCBridge{T} <: Bridges.Variable.AbstractBridge

    RSOCtoSOCBridge implements the following reformulation:

    • $||x||_2^2 \le 2tu$ into $||v||_2 \le w$, with the substitution rules $t = \frac{w}{\sqrt 2} + \frac{v_1}{\sqrt 2}$, $u = \frac{w}{\sqrt 2} - \frac{v_1}{\sqrt 2}$, and $x = (v_2,\ldots,v_N)$.

    Source node

    RSOCtoSOCBridge supports:

    Target node

    RSOCtoSOCBridge creates:

    source
    MathOptInterface.Bridges.Variable.SOCtoRSOCBridge — Type
    SOCtoRSOCBridge{T} <: Bridges.Variable.AbstractBridge

    SOCtoRSOCBridge implements the following reformulation:

    • $||x||_2 \le t$ into $2uv \ge ||w||_2^2$, with the substitution rules $t = \frac{u}{\sqrt 2} + \frac{v}{\sqrt 2}$, $x = (\frac{u}{\sqrt 2} - \frac{v}{\sqrt 2}, w)$.

    Assumptions

    • SOCtoRSOCBridge assumes that $|x| \ge 1$.

    Source node

    SOCtoRSOCBridge supports:

    Target node

    SOCtoRSOCBridge creates:

    source
    MathOptInterface.Bridges.Variable.SetMapBridge — Type
    abstract type SetMapBridge{T,S1,S2} <: AbstractBridge end

    Consider two type of sets, S1 and S2, and a linear mapping A such that the image of a set of type S1 under A is a set of type S2.

    A SetMapBridge{T,S1,S2} is a bridge that substitutes constrained variables in S2 into the image through A of constrained variables in S1.

    The linear map A is described by:

    Implementing a method for these two functions is sufficient to bridge constrained variables. However, in order for the getters and setters of attributes such as dual solutions and starting values to work as well, a method for the following functions must be implemented:

    See the docstrings of each function to see which feature would be missing if it was not implemented for a given bridge.

    source
    MathOptInterface.Bridges.Variable.VectorizeBridge — Type
    VectorizeBridge{T,S} <: Bridges.Variable.AbstractBridge

    VectorizeBridge implements the following reformulations:

    • $x \ge a$ into $[y] \in \mathbb{R}_+$ with the substitution rule $x = a + y$
    • $x \le a$ into $[y] \in \mathbb{R}_-$ with the substitution rule $x = a + y$
    • $x == a$ into $[y] \in \{0\}$ with the substitution rule $x = a + y$

    where T is the coefficient type of a + y.

    Source node

    VectorizeBridge supports:

    Target nodes

    VectorizeBridge creates:

    source
    MathOptInterface.Bridges.Variable.ZerosBridge — Type
    ZerosBridge{T} <: Bridges.Variable.AbstractBridge

    ZerosBridge implements the following reformulation:

    • $x \in \{0\}$ into the substitution rule $x = 0$,

    where T is the coefficient type of 0.

    Source node

    ZerosBridge supports:

    Target nodes

    ZerosBridge does not create target nodes. It replaces all instances of x with 0 via substitution. This means that no variables are created in the underlying model.

    Caveats

    The bridged variables are similar to parameters with zero values. Parameters with non-zero values can be created with constrained variables in MOI.EqualTo by combining a VectorizeBridge and this bridge.

    However, functions modified by ZerosBridge cannot be unbridged. That is, for a given function, we cannot determine if the bridged variables were used.

    A related implication is that this bridge does not support MOI.ConstraintDual. However, if a MOI.Utilities.CachingOptimizer is used, the dual can be determined by the bridged optimizer using MOI.Utilities.get_fallback because the caching optimizer records the unbridged function.

    source
    diff --git a/previews/PR3913/moi/submodules/Bridges/overview/index.html b/previews/PR3913/moi/submodules/Bridges/overview/index.html index d8b1dd92a69..8e6e589d7cf 100644 --- a/previews/PR3913/moi/submodules/Bridges/overview/index.html +++ b/previews/PR3913/moi/submodules/Bridges/overview/index.html @@ -66,4 +66,4 @@ julia> MOI.get(inner_optimizer, MOI.ListOfConstraintTypesPresent()) 1-element Vector{Tuple{Type, Type}}: - (MathOptInterface.VariableIndex, MathOptInterface.Interval{Float64}) + (MathOptInterface.VariableIndex, MathOptInterface.Interval{Float64}) diff --git a/previews/PR3913/moi/submodules/Bridges/reference/index.html b/previews/PR3913/moi/submodules/Bridges/reference/index.html index 9e49fc2d06e..23dfbd520d9 100644 --- a/previews/PR3913/moi/submodules/Bridges/reference/index.html +++ b/previews/PR3913/moi/submodules/Bridges/reference/index.html @@ -221,4 +221,4 @@ cost::Int, )

    As an alternative to variable_node, add a virtual edge to graph that represents adding a free variable, followed by a constraint of type constraint_node, with bridging cost cost.

    Why is this needed?

    Variables can either be added as a variable constrained on creation, or as a free variable which then has a constraint added to it.

    source
    MathOptInterface.Bridges.bridge_index — Function
    bridge_index(graph::Graph, node::VariableNode)::Int
 bridge_index(graph::Graph, node::ConstraintNode)::Int
-bridge_index(graph::Graph, node::ObjectiveNode)::Int

    Return the optimal index of the bridge to chose from node.

    source
    MathOptInterface.Bridges.is_variable_edge_best — Function
    is_variable_edge_best(graph::Graph, node::VariableNode)::Bool

    Return a Bool indicating whether node should be added as a variable constrained on creation, or as a free variable followed by a constraint.

    source
    +bridge_index(graph::Graph, node::ObjectiveNode)::Int

    Return the optimal index of the bridge to chose from node.

    source
    MathOptInterface.Bridges.is_variable_edge_best — Function
    is_variable_edge_best(graph::Graph, node::VariableNode)::Bool

    Return a Bool indicating whether node should be added as a variable constrained on creation, or as a free variable followed by a constraint.

    source
    diff --git a/previews/PR3913/moi/submodules/FileFormats/overview/index.html b/previews/PR3913/moi/submodules/FileFormats/overview/index.html index 8b17133e82e..ea7e4380e98 100644 --- a/previews/PR3913/moi/submodules/FileFormats/overview/index.html +++ b/previews/PR3913/moi/submodules/FileFormats/overview/index.html @@ -158,4 +158,4 @@ path: [variables][1] instance: Dict{String, Any}("NaMe" => "x") schema key: required -schema value: Any["name"] +schema value: Any["name"] diff --git a/previews/PR3913/moi/submodules/FileFormats/reference/index.html b/previews/PR3913/moi/submodules/FileFormats/reference/index.html index 4ab691d931f..73b7b685f1c 100644 --- a/previews/PR3913/moi/submodules/FileFormats/reference/index.html +++ b/previews/PR3913/moi/submodules/FileFormats/reference/index.html @@ -26,4 +26,4 @@ )

    Parse the .sol file filename created by solving model and return a SolFileResults struct.

    The returned struct supports the MOI.get API for querying result attributes such as MOI.TerminationStatus, MOI.VariablePrimal, and MOI.ConstraintDual.

    source
    SolFileResults(
     raw_status::String,
     termination_status::MOI.TerminationStatusCode,
-)

    Return a SolFileResults struct with MOI.RawStatusString set to raw_status, MOI.TerminationStatus set to termination_status, and MOI.PrimalStatus and MOI.DualStatus set to NO_SOLUTION.

    All other attributes are un-set.

    source
    +)

    Return a SolFileResults struct with MOI.RawStatusString set to raw_status, MOI.TerminationStatus set to termination_status, and MOI.PrimalStatus and MOI.DualStatus set to NO_SOLUTION.

    All other attributes are un-set.

    source diff --git a/previews/PR3913/moi/submodules/Nonlinear/overview/index.html b/previews/PR3913/moi/submodules/Nonlinear/overview/index.html index b2417bc61b8..c2946127b3e 100644 --- a/previews/PR3913/moi/submodules/Nonlinear/overview/index.html +++ b/previews/PR3913/moi/submodules/Nonlinear/overview/index.html @@ -184,4 +184,4 @@ Node(NODE_VARIABLE, 1, 1), ], [2.0], - );

    The ordering of the nodes in the tape must satisfy two rules:

    • The children of a node must appear after the parent. This means that the tape is ordered topologically, so that a reverse pass of the nodes evaluates all children nodes before their parent
    • The arguments for a CALL node are ordered in the tape based on the order in which they appear in the function call.

    Design goals

    This is less readable than the other options, but does this data structure meet our design goals?

    Instead of a heap-allocated object for each node, we only have two Vectors for each expression, nodes and values, as well as two constant vectors for the OPERATORS. In addition, all fields are concretely typed, and there are no Union or Any types.

    For our third goal, it is not easy to identify the children of a node, but it is easy to identify the parent of any node. Therefore, we can use Nonlinear.adjacency_matrix to compute a sparse matrix that maps parents to their children.

    The design in practice

    In practice, Node and Expression are exactly Nonlinear.Node and Nonlinear.Expression. However, Nonlinear.NodeType has more fields to account for comparison operators such as :>= and :<=, logic operators such as :&& and :||, nonlinear parameters, and nested subexpressions.

    Moreover, instead of storing the operators as global constants, they are stored in Nonlinear.OperatorRegistry, and it also stores a vector of logic operators and a vector of comparison operators. In addition to Nonlinear.DEFAULT_UNIVARIATE_OPERATORS and Nonlinear.DEFAULT_MULTIVARIATE_OPERATORS, you can register user-defined functions using Nonlinear.register_operator.

    Nonlinear.Model is a struct that stores the Nonlinear.OperatorRegistry, as well as a list of parameters and subexpressions in the model.

    ReverseAD

    Nonlinear.ReverseAD is a submodule for computing derivatives of a nonlinear optimization problem using sparse reverse-mode automatic differentiation (AD).

    This section does not attempt to explain how sparse reverse-mode AD works, but instead explains why MOI contains its own implementation, and highlights notable differences from similar packages.

    Warning

    Don't use the API in ReverseAD to compute derivatives. Instead, create a Nonlinear.Evaluator object with Nonlinear.SparseReverseMode as the backend, and then query the MOI API methods.

    Design goals

    The JuliaDiff organization maintains a list of packages for doing AD in Julia. At last count, there were at least ten packages——not including ReverseAD——for reverse-mode AD in Julia. ReverseAD exists because it has a different set of design goals.

    • Goal: handle scale and sparsity. The types of nonlinear optimization problems that MOI represents can be large scale (10^5 or more functions across 10^5 or more variables) with very sparse derivatives. The ability to compute a sparse Hessian matrix is essential. To the best of our knowledge, ReverseAD is the only reverse-mode AD system in Julia that handles sparsity by default.
    • Goal: limit the scope to improve robustness. Most other AD packages accept arbitrary Julia functions as input and then trace an expression graph using operator overloading. This means they must deal (or detect and ignore) with control flow, I/O, and other vagaries of Julia. In contrast, ReverseAD only accepts functions in the form of Nonlinear.Expression, which greatly limits the range of syntax that it must deal with. By reducing the scope of what we accept as input to functions relevant for mathematical optimization, we can provide a simpler implementation with various performance optimizations.
    • Goal: provide outputs which match what solvers expect. Other AD packages focus on differentiating individual Julia functions. In contrast, ReverseAD has a very specific use-case: to generate outputs needed by the MOI nonlinear API. This means it needs to efficiently compute sparse Hessians, and it needs subexpression handling to avoid recomputing subexpressions that are shared between functions.

    History

    ReverseAD started life as ReverseDiffSparse.jl, development of which began in early 2014(!). This was well before the other AD packages started development. Because we had a well-tested, working AD in JuMP, there was less motivation to contribute to and explore other AD packages. The lack of historical interaction also meant that other packages were not optimized for the types of problems that JuMP is built for (that is, large-scale sparse problems). When we first created MathOptInterface, we kept the AD in JuMP to simplify the transition, and post-poned the development of a first-class nonlinear interface in MathOptInterface.

    Prior to the introduction of Nonlinear, JuMP's nonlinear implementation was a confusing mix of functions and types spread across the code base and in the private _Derivatives submodule. This made it hard to swap the AD system for another. The main motivation for refactoring JuMP to create the Nonlinear submodule in MathOptInterface was to abstract the interface between JuMP and the AD system, allowing us to swap-in and test new AD systems in the future.

    + );

    The ordering of the nodes in the tape must satisfy two rules:

    • The children of a node must appear after the parent. This means that the tape is ordered topologically, so that a reverse pass of the nodes evaluates all children nodes before their parent
    • The arguments for a CALL node are ordered in the tape based on the order in which they appear in the function call.

    Design goals

    This is less readable than the other options, but does this data structure meet our design goals?

    Instead of a heap-allocated object for each node, we only have two Vectors for each expression, nodes and values, as well as two constant vectors for the OPERATORS. In addition, all fields are concretely typed, and there are no Union or Any types.

    For our third goal, it is not easy to identify the children of a node, but it is easy to identify the parent of any node. Therefore, we can use Nonlinear.adjacency_matrix to compute a sparse matrix that maps parents to their children.

    The design in practice

    In practice, Node and Expression are exactly Nonlinear.Node and Nonlinear.Expression. However, Nonlinear.NodeType has more fields to account for comparison operators such as :>= and :<=, logic operators such as :&& and :||, nonlinear parameters, and nested subexpressions.

    Moreover, instead of storing the operators as global constants, they are stored in Nonlinear.OperatorRegistry, and it also stores a vector of logic operators and a vector of comparison operators. In addition to Nonlinear.DEFAULT_UNIVARIATE_OPERATORS and Nonlinear.DEFAULT_MULTIVARIATE_OPERATORS, you can register user-defined functions using Nonlinear.register_operator.

    Nonlinear.Model is a struct that stores the Nonlinear.OperatorRegistry, as well as a list of parameters and subexpressions in the model.

    ReverseAD

    Nonlinear.ReverseAD is a submodule for computing derivatives of a nonlinear optimization problem using sparse reverse-mode automatic differentiation (AD).

    This section does not attempt to explain how sparse reverse-mode AD works, but instead explains why MOI contains its own implementation, and highlights notable differences from similar packages.

    Warning

    Don't use the API in ReverseAD to compute derivatives. Instead, create a Nonlinear.Evaluator object with Nonlinear.SparseReverseMode as the backend, and then query the MOI API methods.

    Design goals

    The JuliaDiff organization maintains a list of packages for doing AD in Julia. At last count, there were at least ten packages——not including ReverseAD——for reverse-mode AD in Julia. ReverseAD exists because it has a different set of design goals.

    • Goal: handle scale and sparsity. The types of nonlinear optimization problems that MOI represents can be large scale (10^5 or more functions across 10^5 or more variables) with very sparse derivatives. The ability to compute a sparse Hessian matrix is essential. To the best of our knowledge, ReverseAD is the only reverse-mode AD system in Julia that handles sparsity by default.
    • Goal: limit the scope to improve robustness. Most other AD packages accept arbitrary Julia functions as input and then trace an expression graph using operator overloading. This means they must deal (or detect and ignore) with control flow, I/O, and other vagaries of Julia. In contrast, ReverseAD only accepts functions in the form of Nonlinear.Expression, which greatly limits the range of syntax that it must deal with. By reducing the scope of what we accept as input to functions relevant for mathematical optimization, we can provide a simpler implementation with various performance optimizations.
    • Goal: provide outputs which match what solvers expect. Other AD packages focus on differentiating individual Julia functions. In contrast, ReverseAD has a very specific use-case: to generate outputs needed by the MOI nonlinear API. This means it needs to efficiently compute sparse Hessians, and it needs subexpression handling to avoid recomputing subexpressions that are shared between functions.

    History

    ReverseAD started life as ReverseDiffSparse.jl, development of which began in early 2014(!). This was well before the other AD packages started development. Because we had a well-tested, working AD in JuMP, there was less motivation to contribute to and explore other AD packages. The lack of historical interaction also meant that other packages were not optimized for the types of problems that JuMP is built for (that is, large-scale sparse problems). When we first created MathOptInterface, we kept the AD in JuMP to simplify the transition, and post-poned the development of a first-class nonlinear interface in MathOptInterface.

    Prior to the introduction of Nonlinear, JuMP's nonlinear implementation was a confusing mix of functions and types spread across the code base and in the private _Derivatives submodule. This made it hard to swap the AD system for another. The main motivation for refactoring JuMP to create the Nonlinear submodule in MathOptInterface was to abstract the interface between JuMP and the AD system, allowing us to swap-in and test new AD systems in the future.

    diff --git a/previews/PR3913/moi/submodules/Nonlinear/reference/index.html b/previews/PR3913/moi/submodules/Nonlinear/reference/index.html index 1567d9ae5b7..462461e1124 100644 --- a/previews/PR3913/moi/submodules/Nonlinear/reference/index.html +++ b/previews/PR3913/moi/submodules/Nonlinear/reference/index.html @@ -236,4 +236,4 @@ julia> MOI.initialize(evaluator, Symbol[]) julia> MOI.Nonlinear.ordinal_index(evaluator, c2) # Returns 1 -1source +1source diff --git a/previews/PR3913/moi/submodules/Test/overview/index.html b/previews/PR3913/moi/submodules/Test/overview/index.html index 1b2ffb5458a..4f5ee261240 100644 --- a/previews/PR3913/moi/submodules/Test/overview/index.html +++ b/previews/PR3913/moi/submodules/Test/overview/index.html @@ -167,4 +167,4 @@ ), ) return -end

    Finally, you also need to implement Test.version_added. If we added this test when the latest released version of MOI was v0.10.5, define:

    version_added(::typeof(test_unit_optimize!_twice)) = v"0.10.6"

    Step 6

    Commit the changes to git from ~/.julia/dev/MathOptInterface and submit the PR for review.

    Tip

    If you need help writing a test, open an issue on GitHub, or ask the Developer Chatroom.

    +end

    Finally, you also need to implement Test.version_added. If we added this test when the latest released version of MOI was v0.10.5, define:

    version_added(::typeof(test_unit_optimize!_twice)) = v"0.10.6"

    Step 6

    Commit the changes to git from ~/.julia/dev/MathOptInterface and submit the PR for review.

    Tip

    If you need help writing a test, open an issue on GitHub, or ask the Developer Chatroom.

    diff --git a/previews/PR3913/moi/submodules/Test/reference/index.html b/previews/PR3913/moi/submodules/Test/reference/index.html index 6cfe602dae2..42a128b4092 100644 --- a/previews/PR3913/moi/submodules/Test/reference/index.html +++ b/previews/PR3913/moi/submodules/Test/reference/index.html @@ -63,4 +63,4 @@ \text{subject to}\ & x_1 * x_2 * x_3 * x_4 \ge 25 \\ & x_1^2 + x_2^2 + x_3^2 + x_4^2 = 40 \\ & 1 \le x_1, x_2, x_3, x_4 \le 5 -\end{aligned}\]

    The optimal solution is [1.000, 4.743, 3.821, 1.379].

    source +\end{aligned}\]

    The optimal solution is [1.000, 4.743, 3.821, 1.379].

    source diff --git a/previews/PR3913/moi/submodules/Utilities/overview/index.html b/previews/PR3913/moi/submodules/Utilities/overview/index.html index 3fa4a9df768..a74178da1fb 100644 --- a/previews/PR3913/moi/submodules/Utilities/overview/index.html +++ b/previews/PR3913/moi/submodules/Utilities/overview/index.html @@ -378,4 +378,4 @@ index_map = MOI.copy_to(dest, src) for (F, S) in MOI.get(src, MOI.ListOfConstraintTypesPresent()) function_barrier(dest, src, index_map[F, S]) -end +end diff --git a/previews/PR3913/moi/submodules/Utilities/reference/index.html b/previews/PR3913/moi/submodules/Utilities/reference/index.html index 1bfd84891e3..64556c07845 100644 --- a/previews/PR3913/moi/submodules/Utilities/reference/index.html +++ b/previews/PR3913/moi/submodules/Utilities/reference/index.html @@ -91,7 +91,7 @@ typeof(CleverDicts.key_to_index), typeof(CleverDicts.index_to_key), } -end

    A struct storing F-in-S constraints as a mapping between the constraint indices to the corresponding tuple of function and set.

    source
    MathOptInterface.Utilities.@struct_of_constraints_by_function_types — Macro
    Utilities.@struct_of_constraints_by_function_types(name, func_types...)

    Given a vector of n function types (F1, F2,..., Fn) in func_types, defines a subtype of StructOfConstraints of name name and which type parameters {T, C1, C2, ..., Cn}. It contains n field where the ith field has type Ci and stores the constraints of function type Fi.

    The expression Fi can also be a union in which case any constraint for which the function type is in the union is stored in the field with type Ci.

    source
    MathOptInterface.Utilities.@struct_of_constraints_by_set_types — Macro
    Utilities.@struct_of_constraints_by_set_types(name, func_types...)

    Given a vector of n set types (S1, S2,..., Sn) in func_types, defines a subtype of StructOfConstraints of name name and which type parameters {T, C1, C2, ..., Cn}. It contains n field where the ith field has type Ci and stores the constraints of set type Si. The expression Si can also be a union in which case any constraint for which the set type is in the union is stored in the field with type Ci. This can be useful if Ci is a MatrixOfConstraints in order to concatenate the coefficients of constraints of several different set types in the same matrix.

    source
    MathOptInterface.Utilities.struct_of_constraint_code — Function
    struct_of_constraint_code(struct_name, types, field_types = nothing)

    Given a vector of n Union{SymbolFun,_UnionSymbolFS{SymbolFun}} or Union{SymbolSet,_UnionSymbolFS{SymbolSet}} in types, defines a subtype of StructOfConstraints of name name and which type parameters {T, F1, F2, ..., Fn} if field_types is nothing and a {T} otherwise. It contains n field where the ith field has type Ci if field_types is nothing and type field_types[i] otherwise. If types is vector of Union{SymbolFun,_UnionSymbolFS{SymbolFun}} (resp. Union{SymbolSet,_UnionSymbolFS{SymbolSet}}) then the constraints of that function (resp. set) type are stored in the corresponding field.

    This function is used by the macros @model, @struct_of_constraints_by_function_types and @struct_of_constraints_by_set_types.

    source

    Caching optimizer

    MathOptInterface.Utilities.CachingOptimizer — Type
    CachingOptimizer

    CachingOptimizer is an intermediate layer that stores a cache of the model and links it with an optimizer. It supports incremental model construction and modification even when the optimizer doesn't.

    Constructors

        CachingOptimizer(cache::MOI.ModelLike, optimizer::AbstractOptimizer)

    Creates a CachingOptimizer in AUTOMATIC mode, with the optimizer optimizer.

    The type of the optimizer returned is CachingOptimizer{typeof(optimizer), typeof(cache)} so it does not support the function reset_optimizer(::CachingOptimizer, new_optimizer) if the type of new_optimizer is different from the type of optimizer.

        CachingOptimizer(cache::MOI.ModelLike, mode::CachingOptimizerMode)

    Creates a CachingOptimizer in the NO_OPTIMIZER state and mode mode.

    The type of the optimizer returned is CachingOptimizer{MOI.AbstractOptimizer,typeof(cache)} so it does support the function reset_optimizer(::CachingOptimizer, new_optimizer) if the type of new_optimizer is different from the type of optimizer.

    About the type

    States

    A CachingOptimizer may be in one of three possible states (CachingOptimizerState):

    • NO_OPTIMIZER: The CachingOptimizer does not have any optimizer.
    • EMPTY_OPTIMIZER: The CachingOptimizer has an empty optimizer. The optimizer is not synchronized with the cached model.
    • ATTACHED_OPTIMIZER: The CachingOptimizer has an optimizer, and it is synchronized with the cached model.

    Modes

    A CachingOptimizer has two modes of operation (CachingOptimizerMode):

    • MANUAL: The only methods that change the state of the CachingOptimizer are Utilities.reset_optimizer, Utilities.drop_optimizer, and Utilities.attach_optimizer. Attempting to perform an operation in the incorrect state results in an error.
    • AUTOMATIC: The CachingOptimizer changes its state when necessary. For example, optimize! will automatically call attach_optimizer (an optimizer must have been previously set). Attempting to add a constraint or perform a modification not supported by the optimizer results in a drop to EMPTY_OPTIMIZER mode.
    source
    MathOptInterface.Utilities.attach_optimizer — Function
    attach_optimizer(model::CachingOptimizer)

    Attaches the optimizer to model, copying all model data into it. Can be called only from the EMPTY_OPTIMIZER state. If the copy succeeds, the CachingOptimizer will be in state ATTACHED_OPTIMIZER after the call, otherwise an error is thrown; see MOI.copy_to for more details on which errors can be thrown.

    source
    MOIU.attach_optimizer(model::GenericModel)

    Call MOIU.attach_optimizer on the backend of model.

    Cannot be called in direct mode.

    source
    MathOptInterface.Utilities.reset_optimizer — Function
    reset_optimizer(m::CachingOptimizer, optimizer::MOI.AbstractOptimizer)

    Sets or resets m to have the given empty optimizer optimizer.

    Can be called from any state. An assertion error will be thrown if optimizer is not empty.

    The CachingOptimizer m will be in state EMPTY_OPTIMIZER after the call.

    source
    reset_optimizer(m::CachingOptimizer)

    Detaches and empties the current optimizer. Can be called from ATTACHED_OPTIMIZER or EMPTY_OPTIMIZER state. The CachingOptimizer will be in state EMPTY_OPTIMIZER after the call.

    source
    MOIU.reset_optimizer(model::GenericModel, optimizer::MOI.AbstractOptimizer)

    Call MOIU.reset_optimizer on the backend of model.

    Cannot be called in direct mode.

    source
    MOIU.reset_optimizer(model::GenericModel)

    Call MOIU.reset_optimizer on the backend of model.

    Cannot be called in direct mode.

    source
    MathOptInterface.Utilities.drop_optimizer — Function
    drop_optimizer(m::CachingOptimizer)

    Drops the optimizer, if one is present. Can be called from any state. The CachingOptimizer will be in state NO_OPTIMIZER after the call.

    source
    MOIU.drop_optimizer(model::GenericModel)

    Call MOIU.drop_optimizer on the backend of model.

    Cannot be called in direct mode.

    source

    Mock optimizer

    Printing

    MathOptInterface.Utilities.latex_formulation — Function
    latex_formulation(model::MOI.ModelLike; kwargs...)

    Wrap model in a type so that it can be pretty-printed as text/latex in a notebook like IJulia, or in Documenter.

    To render the model, end the cell with latex_formulation(model), or call display(latex_formulation(model)) in to force the display of the model from inside a function.

    Possible keyword arguments are:

    • simplify_coefficients : Simplify coefficients if possible by omitting them or removing trailing zeros.
    • default_name : The name given to variables with an empty name.
    • print_types : Print the MOI type of each function and set for clarity.
    source

    Copy utilities

    MathOptInterface.Utilities.ModelFilter — Type
    ModelFilter(filter::Function, model::MOI.ModelLike)

    A layer to filter out various components of model.

    The filter function takes a single argument, which is each element from the list returned by the attributes below. It returns true if the element should be visible in the filtered model and false otherwise.

    The components that are filtered are:

    • Entire constraint types via:
      • MOI.ListOfConstraintTypesPresent
    • Individual constraints via:
      • MOI.ListOfConstraintIndices{F,S}
    • Specific attributes via:
      • MOI.ListOfModelAttributesSet
      • MOI.ListOfConstraintAttributesSet
      • MOI.ListOfVariableAttributesSet
    Warning

    The list of attributes filtered may change in a future release. You should write functions that are generic and not limited to the five types listed above. Thus, you should probably define a fallback filter(::Any) = true.

    See below for examples of how this works.

    Note

    This layer has a limited scope. It is intended by be used in conjunction with MOI.copy_to.

    Example: copy model excluding integer constraints

    Use the do syntax to provide a single function.

    filtered_src = MOI.Utilities.ModelFilter(src) do item
+end

    A struct storing F-in-S constraints as a mapping between the constraint indices to the corresponding tuple of function and set.

    source
    MathOptInterface.Utilities.@struct_of_constraints_by_function_types — Macro
    Utilities.@struct_of_constraints_by_function_types(name, func_types...)

    Given a vector of n function types (F1, F2,..., Fn) in func_types, defines a subtype of StructOfConstraints of name name and which type parameters {T, C1, C2, ..., Cn}. It contains n field where the ith field has type Ci and stores the constraints of function type Fi.

    The expression Fi can also be a union in which case any constraint for which the function type is in the union is stored in the field with type Ci.

    source
    MathOptInterface.Utilities.@struct_of_constraints_by_set_types — Macro
    Utilities.@struct_of_constraints_by_set_types(name, func_types...)

    Given a vector of n set types (S1, S2,..., Sn) in func_types, defines a subtype of StructOfConstraints of name name and which type parameters {T, C1, C2, ..., Cn}. It contains n field where the ith field has type Ci and stores the constraints of set type Si. The expression Si can also be a union in which case any constraint for which the set type is in the union is stored in the field with type Ci. This can be useful if Ci is a MatrixOfConstraints in order to concatenate the coefficients of constraints of several different set types in the same matrix.

    source
    MathOptInterface.Utilities.struct_of_constraint_code — Function
    struct_of_constraint_code(struct_name, types, field_types = nothing)

    Given a vector of n Union{SymbolFun,_UnionSymbolFS{SymbolFun}} or Union{SymbolSet,_UnionSymbolFS{SymbolSet}} in types, defines a subtype of StructOfConstraints of name name and which type parameters {T, F1, F2, ..., Fn} if field_types is nothing and a {T} otherwise. It contains n field where the ith field has type Ci if field_types is nothing and type field_types[i] otherwise. If types is vector of Union{SymbolFun,_UnionSymbolFS{SymbolFun}} (resp. Union{SymbolSet,_UnionSymbolFS{SymbolSet}}) then the constraints of that function (resp. set) type are stored in the corresponding field.

    This function is used by the macros @model, @struct_of_constraints_by_function_types and @struct_of_constraints_by_set_types.

    source

    Caching optimizer

    MathOptInterface.Utilities.CachingOptimizer — Type
    CachingOptimizer

    CachingOptimizer is an intermediate layer that stores a cache of the model and links it with an optimizer. It supports incremental model construction and modification even when the optimizer doesn't.

    Constructors

        CachingOptimizer(cache::MOI.ModelLike, optimizer::AbstractOptimizer)

    Creates a CachingOptimizer in AUTOMATIC mode, with the optimizer optimizer.

    The type of the optimizer returned is CachingOptimizer{typeof(optimizer), typeof(cache)} so it does not support the function reset_optimizer(::CachingOptimizer, new_optimizer) if the type of new_optimizer is different from the type of optimizer.

        CachingOptimizer(cache::MOI.ModelLike, mode::CachingOptimizerMode)

    Creates a CachingOptimizer in the NO_OPTIMIZER state and mode mode.

    The type of the optimizer returned is CachingOptimizer{MOI.AbstractOptimizer,typeof(cache)} so it does support the function reset_optimizer(::CachingOptimizer, new_optimizer) if the type of new_optimizer is different from the type of optimizer.

    About the type

    States

    A CachingOptimizer may be in one of three possible states (CachingOptimizerState):

    • NO_OPTIMIZER: The CachingOptimizer does not have any optimizer.
    • EMPTY_OPTIMIZER: The CachingOptimizer has an empty optimizer. The optimizer is not synchronized with the cached model.
    • ATTACHED_OPTIMIZER: The CachingOptimizer has an optimizer, and it is synchronized with the cached model.

    Modes

    A CachingOptimizer has two modes of operation (CachingOptimizerMode):

    • MANUAL: The only methods that change the state of the CachingOptimizer are Utilities.reset_optimizer, Utilities.drop_optimizer, and Utilities.attach_optimizer. Attempting to perform an operation in the incorrect state results in an error.
    • AUTOMATIC: The CachingOptimizer changes its state when necessary. For example, optimize! will automatically call attach_optimizer (an optimizer must have been previously set). Attempting to add a constraint or perform a modification not supported by the optimizer results in a drop to EMPTY_OPTIMIZER mode.
    source
    MathOptInterface.Utilities.attach_optimizer — Function
    attach_optimizer(model::CachingOptimizer)

    Attaches the optimizer to model, copying all model data into it. Can be called only from the EMPTY_OPTIMIZER state. If the copy succeeds, the CachingOptimizer will be in state ATTACHED_OPTIMIZER after the call, otherwise an error is thrown; see MOI.copy_to for more details on which errors can be thrown.

    source
    MOIU.attach_optimizer(model::GenericModel)

    Call MOIU.attach_optimizer on the backend of model.

    Cannot be called in direct mode.

    source
    MathOptInterface.Utilities.reset_optimizer — Function
    reset_optimizer(m::CachingOptimizer, optimizer::MOI.AbstractOptimizer)

    Sets or resets m to have the given empty optimizer optimizer.

    Can be called from any state. An assertion error will be thrown if optimizer is not empty.

    The CachingOptimizer m will be in state EMPTY_OPTIMIZER after the call.

    source
    reset_optimizer(m::CachingOptimizer)

    Detaches and empties the current optimizer. Can be called from ATTACHED_OPTIMIZER or EMPTY_OPTIMIZER state. The CachingOptimizer will be in state EMPTY_OPTIMIZER after the call.

    source
    MOIU.reset_optimizer(model::GenericModel, optimizer::MOI.AbstractOptimizer)

    Call MOIU.reset_optimizer on the backend of model.

    Cannot be called in direct mode.

    source
    MOIU.reset_optimizer(model::GenericModel)

    Call MOIU.reset_optimizer on the backend of model.

    Cannot be called in direct mode.

    source
    MathOptInterface.Utilities.drop_optimizer — Function
    drop_optimizer(m::CachingOptimizer)

    Drops the optimizer, if one is present. Can be called from any state. The CachingOptimizer will be in state NO_OPTIMIZER after the call.

    source
    MOIU.drop_optimizer(model::GenericModel)

    Call MOIU.drop_optimizer on the backend of model.

    Cannot be called in direct mode.

    source

    Mock optimizer

    Printing

    MathOptInterface.Utilities.latex_formulation — Function
    latex_formulation(model::MOI.ModelLike; kwargs...)

    Wrap model in a type so that it can be pretty-printed as text/latex in a notebook like IJulia, or in Documenter.

    To render the model, end the cell with latex_formulation(model), or call display(latex_formulation(model)) in to force the display of the model from inside a function.

    Possible keyword arguments are:

    • simplify_coefficients : Simplify coefficients if possible by omitting them or removing trailing zeros.
    • default_name : The name given to variables with an empty name.
    • print_types : Print the MOI type of each function and set for clarity.
    source

    Copy utilities

    MathOptInterface.Utilities.ModelFilter — Type
    ModelFilter(filter::Function, model::MOI.ModelLike)

    A layer to filter out various components of model.

    The filter function takes a single argument, which is each element from the list returned by the attributes below. It returns true if the element should be visible in the filtered model and false otherwise.

    The components that are filtered are:

    • Entire constraint types via:
      • MOI.ListOfConstraintTypesPresent
    • Individual constraints via:
      • MOI.ListOfConstraintIndices{F,S}
    • Specific attributes via:
      • MOI.ListOfModelAttributesSet
      • MOI.ListOfConstraintAttributesSet
      • MOI.ListOfVariableAttributesSet
    Warning

    The list of attributes filtered may change in a future release. You should write functions that are generic and not limited to the five types listed above. Thus, you should probably define a fallback filter(::Any) = true.

    See below for examples of how this works.

    Note

    This layer has a limited scope. It is intended by be used in conjunction with MOI.copy_to.

    Example: copy model excluding integer constraints

    Use the do syntax to provide a single function.

    filtered_src = MOI.Utilities.ModelFilter(src) do item
     return item != (MOI.VariableIndex, MOI.Integer)
 end
 MOI.copy_to(dest, filtered_src)

    Example: copy model excluding names

    Use type dispatch to simplify the implementation:

    my_filter(::Any) = true  # Note the generic fallback
@@ -343,4 +343,4 @@
 For performance, it is recommended that the inner loop lies in a separate
 function to guarantee type-stability.
 
-If you want an iterator of all current outer keys, use [`outer_keys`](@ref).
    source
    +If you want an iterator of all current outer keys, use [`outer_keys`](@ref).source diff --git a/previews/PR3913/moi/tutorials/bridging_constraint/index.html b/previews/PR3913/moi/tutorials/bridging_constraint/index.html index 884f830de5d..a06a1220651 100644 --- a/previews/PR3913/moi/tutorials/bridging_constraint/index.html +++ b/previews/PR3913/moi/tutorials/bridging_constraint/index.html @@ -103,4 +103,4 @@ end

    Bridge deletion

    When a bridge is deleted, the constraints it added must be deleted too.

    function delete(model::ModelLike, bridge::SignBridge)
     delete(model, bridge.constraint)
     return
-end
    +end diff --git a/previews/PR3913/moi/tutorials/example/index.html b/previews/PR3913/moi/tutorials/example/index.html index 14820938a1e..1d0ffb12486 100644 --- a/previews/PR3913/moi/tutorials/example/index.html +++ b/previews/PR3913/moi/tutorials/example/index.html @@ -46,4 +46,4 @@ 3-element Vector{Float64}: 1.0 1.0 - 1.0 + 1.0 diff --git a/previews/PR3913/moi/tutorials/implementing/index.html b/previews/PR3913/moi/tutorials/implementing/index.html index 0fffcbe07ef..b1ab926e619 100644 --- a/previews/PR3913/moi/tutorials/implementing/index.html +++ b/previews/PR3913/moi/tutorials/implementing/index.html @@ -115,4 +115,4 @@ n = # Code to get NumberOfObjectives return n end

    Then, the user can write:

    model = Gurobi.Optimizer()
-MOI.set(model, Gurobi.NumberofObjectives(), 3)
    +MOI.set(model, Gurobi.NumberofObjectives(), 3) diff --git a/previews/PR3913/moi/tutorials/latency/index.html b/previews/PR3913/moi/tutorials/latency/index.html index b88d38a5283..f4d364c9a6f 100644 --- a/previews/PR3913/moi/tutorials/latency/index.html +++ b/previews/PR3913/moi/tutorials/latency/index.html @@ -130,4 +130,4 @@ end

    You can create a flame-graph via

    using SnoopCompile
 tinf = @snoopi_deep example_diet(GLPK.Optimizer, true)
 using ProfileView
-ProfileView.view(flamegraph(tinf))

    Here's how things looked in mid-August 2021: flamegraph

    There are a few opportunities for improvement (non-red flames, particularly on the right). But the main problem is a large red (non-precompilable due to method ownership) flame.

    +ProfileView.view(flamegraph(tinf))

    Here's how things looked in mid-August 2021: flamegraph

    There are a few opportunities for improvement (non-red flames, particularly on the right). But the main problem is a large red (non-precompilable due to method ownership) flame.

    diff --git a/previews/PR3913/moi/tutorials/manipulating_expressions/index.html b/previews/PR3913/moi/tutorials/manipulating_expressions/index.html index 9763929937e..b065b2243ec 100644 --- a/previews/PR3913/moi/tutorials/manipulating_expressions/index.html +++ b/previews/PR3913/moi/tutorials/manipulating_expressions/index.html @@ -23,4 +23,4 @@ 2-element Vector{MathOptInterface.ScalarAffineFunction{Int64}}: (2) + (1) MOI.VariableIndex(1) (4) + (2) MOI.VariableIndex(1)
    Note

    Utilities.eachscalar returns an iterator on the dimensions, which serves the same purpose as Utilities.scalarize.

    output_dimension returns the number of dimensions of the output of a function:

    julia> MOI.output_dimension(g)
-2
    +2 diff --git a/previews/PR3913/moi/tutorials/mathprogbase/index.html b/previews/PR3913/moi/tutorials/mathprogbase/index.html index 02b5709b7ff..07c5e6c4f2e 100644 --- a/previews/PR3913/moi/tutorials/mathprogbase/index.html +++ b/previews/PR3913/moi/tutorials/mathprogbase/index.html @@ -55,4 +55,4 @@ objval = objective_value(model), sol = value.(x) ) -end +end diff --git a/previews/PR3913/packages/Alpine/index.html b/previews/PR3913/packages/Alpine/index.html index a2b535fc0ac..fadc4db9ff4 100644 --- a/previews/PR3913/packages/Alpine/index.html +++ b/previews/PR3913/packages/Alpine/index.html @@ -46,4 +46,4 @@ author={Kim, Jongeun and Richard, Jean-Philippe P. and Tawarmalani, Mohit}, eprinttype={Optimization Online}, date={2022} -} +} diff --git a/previews/PR3913/packages/AmplNLWriter/index.html b/previews/PR3913/packages/AmplNLWriter/index.html index f0f6484b9cc..67f3536c10d 100644 --- a/previews/PR3913/packages/AmplNLWriter/index.html +++ b/previews/PR3913/packages/AmplNLWriter/index.html @@ -12,4 +12,4 @@ import Bonmin_jll model = Model(() -> AmplNLWriter.Optimizer(Bonmin_jll.amplexe)) set_attribute(model, "bonmin.nlp_log_level", 0)

    opt files

    Some options need to be specified via an .opt file.

    This file must be located in the current working directory whenever the model is solved.

    The .opt file must be named after the name of the solver, for example, bonmin.opt, and each line must contain an option name and the desired value, separated by a space.

    For example, to set the absolute and relative tolerances in Couenne to 1 and 0.05 respectively, the couenne.opt file should contain:

    allowable_gap 1
-allowable_fraction_gap 0.05
    +allowable_fraction_gap 0.05 diff --git a/previews/PR3913/packages/BARON/index.html b/previews/PR3913/packages/BARON/index.html index 4a15672e547..3335a310a65 100644 --- a/previews/PR3913/packages/BARON/index.html +++ b/previews/PR3913/packages/BARON/index.html @@ -6,4 +6,4 @@
    GitHub

    BARON.jl

    Build Status codecov

    BARON.jl is a wrapper for BARON by The Optimization Firm.

    Affiliation

    This wrapper is maintained by the JuMP community and is not officially supported by The Optimization Firm.

    Getting help

    If you need help, please ask a question on the JuMP community forum.

    If you have a reproducible example of a bug, please open a GitHub issue.

    License

    BARON.jl is licensed under the MIT License.

    The underlying solver is a closed-source commercial product for which you must obtain a license from The Optimization Firm, although a small trial version is available for free.

    Installation

    First, download a copy of the BARON solver and unpack the executable in a location of your choosing.

    Once installed, set the BARON_EXEC environment variable pointing to the BARON executable (full path, including file name as it differs across platforms), and run Pkg.add("BARON"). For example:

    ENV["BARON_EXEC"] = "/path/to/baron.exe"
 using Pkg
 Pkg.add("BARON")

    The baronlice.txt license file should be placed in the same directory as the BARON executable, or in your current working directory.

    Use with JuMP

    using JuMP, BARON
-model = Model(BARON.Optimizer)

    MathOptInterface API

    The BARON optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    +model = Model(BARON.Optimizer)

    MathOptInterface API

    The BARON optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    diff --git a/previews/PR3913/packages/BilevelJuMP/index.html b/previews/PR3913/packages/BilevelJuMP/index.html index b9368321fd7..830cd5d2633 100644 --- a/previews/PR3913/packages/BilevelJuMP/index.html +++ b/previews/PR3913/packages/BilevelJuMP/index.html @@ -34,4 +34,4 @@ objective_value(model) # = 3 * (3.5 * 8/15) + 8/15 # = 6.13... value(x) # = 3.5 * 8/15 # = 1.86... -value(y) # = 8/15 # = 0.53... +value(y) # = 8/15 # = 0.53... diff --git a/previews/PR3913/packages/CATrustRegionMethod/index.html b/previews/PR3913/packages/CATrustRegionMethod/index.html index 062605424cb..66af4a80a7b 100644 --- a/previews/PR3913/packages/CATrustRegionMethod/index.html +++ b/previews/PR3913/packages/CATrustRegionMethod/index.html @@ -18,4 +18,4 @@ # Retrieve the solver instance optimizer = backend(model).optimizer.model # Algorithm stats (total function evalation, ...) -algorithm_counter = optimizer.inner.algorithm_counter

    CUTEst test set

    To test our solver on CUTEst test set, please use the script:

    solve_cutest.jl

    To see the meaning of each argument:

    $ julia --project=. scripts/solve_cutest.jl --help

    Here is a simple example:

    $ julia --project=. scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true

    Plots for CUTEst test set

    $ julia --project=. scripts/plot_CUTEst_results.jl --output_dir ./scripts/benchmark/results/cutest

    Instructions for reproducing our experiments

    CUTEst test set

    $ julia --project=. scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true
    $ julia --project=. scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true --θ 0.0
    $ julia --project=. scripts/run_ablation_study.jl --output_dir ./scripts/benchmark/results_ablation_study/cutest --default_problems true

    Examples

    Examples can be found under the test directory

    References

    Citing

    ```markdown If you use our method in your research, you are kindly asked to cite the relevant papers:

    @article{hamad2024simple, title={A simple and practical adaptive trust-region method}, author={Hamad, Fadi and Hinder, Oliver}, journal={arXiv preprint arXiv:2412.02079}, year={2024} }

    @article{hamad2022consistently, title={A consistently adaptive trust-region method}, author={Hamad, Fadi and Hinder, Oliver}, journal={Advances in Neural Information Processing Systems}, volume={35}, pages={6640–6653}, year={2022} }

    +algorithm_counter = optimizer.inner.algorithm_counter

    CUTEst test set

    To test our solver on CUTEst test set, please use the script:

    solve_cutest.jl

    To see the meaning of each argument:

    $ julia --project=. scripts/solve_cutest.jl --help

    Here is a simple example:

    $ julia --project=. scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true

    Plots for CUTEst test set

    $ julia --project=. scripts/plot_CUTEst_results.jl --output_dir ./scripts/benchmark/results/cutest

    Instructions for reproducing our experiments

    CUTEst test set

    $ julia --project=. scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true
    $ julia --project=. scripts/solve_cutest.jl --output_dir ./scripts/benchmark/results/cutest --default_problems true --θ 0.0
    $ julia --project=. scripts/run_ablation_study.jl --output_dir ./scripts/benchmark/results_ablation_study/cutest --default_problems true

    Examples

    Examples can be found under the test directory

    References

    Citing

    ```markdown If you use our method in your research, you are kindly asked to cite the relevant papers:

    @article{hamad2024simple, title={A simple and practical adaptive trust-region method}, author={Hamad, Fadi and Hinder, Oliver}, journal={arXiv preprint arXiv:2412.02079}, year={2024} }

    @article{hamad2022consistently, title={A consistently adaptive trust-region method}, author={Hamad, Fadi and Hinder, Oliver}, journal={Advances in Neural Information Processing Systems}, volume={35}, pages={6640–6653}, year={2022} }

    diff --git a/previews/PR3913/packages/CDCS/index.html b/previews/PR3913/packages/CDCS/index.html index d0beba106a9..5a6c6b5ca30 100644 --- a/previews/PR3913/packages/CDCS/index.html +++ b/previews/PR3913/packages/CDCS/index.html @@ -27,4 +27,4 @@ mat"cdcsInstall" end -julia> mat"savepath" +julia> mat"savepath" diff --git a/previews/PR3913/packages/CDDLib/index.html b/previews/PR3913/packages/CDDLib/index.html index 72377eb86ec..e736c660e26 100644 --- a/previews/PR3913/packages/CDDLib/index.html +++ b/previews/PR3913/packages/CDDLib/index.html @@ -6,4 +6,4 @@
    GitHub

    CDDLib

    CDDLib.jl is a wrapper for cddlib.

    CDDLib.jl can be used with C API of cddlib, the higher level interface of Polyhedra.jl, or as a linear programming solver with JuMP or MathOptInterface.

    Problem description

    As written in the README of cddlib:

    The C-library cddlib is a C implementation of the Double Description Method of Motzkin et al. for generating all vertices (that is, extreme points) and extreme rays of a general convex polyhedron in R^d given by a system of linear inequalities:

    P = { x=(x1, ..., xd)^T :  b - A  x  >= 0 }

    where A is a given m x d real matrix, b is a given m-vector and 0 is the m-vector of all zeros.

    The program can be used for the reverse operation (that is, convex hull computation). This means that one can move back and forth between an inequality representation and a generator (that is, vertex and ray) representation of a polyhedron with cdd. Also, cdd can solve a linear programming problem, that is, a problem of maximizing and minimizing a linear function over P.

    License

    CDDLib.jl is licensed under the GPL v2 license.

    The underlying solver, cddlib/cddlib is also licensed under the GPL v2 license.

    Installation

    Install CDDLib.jl using the Julia package manager:

    import Pkg
 Pkg.add("CDDLib")

    Building the package will download binaries of cddlib that are provided by cddlib_jll.jl.

    Use with JuMP

    Use CDDLib.Optimizer{Float64} to use CDDLib.jl with JuMP:

    using JuMP, CDDLib
 model = Model(CDDLib.Optimizer{Float64})

    When using CDDLib.jl with MathOptInterface, you can pass a different number type:

    using MathOptInterface, CDDLib
-model = CDDLib.Optimizer{Rational{BigInt}}()

    Debugging

    CDDLib.jl uses two global Boolean variables to enable debugging outputs: debug and log.

    You can query the value of debug and log with get_debug and get_log, and set their values with set_debug and set_log.

    +model = CDDLib.Optimizer{Rational{BigInt}}()

    Debugging

    CDDLib.jl uses two global Boolean variables to enable debugging outputs: debug and log.

    You can query the value of debug and log with get_debug and get_log, and set their values with set_debug and set_log.

    diff --git a/previews/PR3913/packages/COPT/index.html b/previews/PR3913/packages/COPT/index.html index 65f2c93d1cc..7297bf5a367 100644 --- a/previews/PR3913/packages/COPT/index.html +++ b/previews/PR3913/packages/COPT/index.html @@ -39,4 +39,4 @@ @show value.(X) @show value.(z) @show shadow_price(c1) -@show shadow_price(c2) +@show shadow_price(c2) diff --git a/previews/PR3913/packages/COSMO/index.html b/previews/PR3913/packages/COSMO/index.html index b3954a146bf..aeca918fff1 100644 --- a/previews/PR3913/packages/COSMO/index.html +++ b/previews/PR3913/packages/COSMO/index.html @@ -34,4 +34,4 @@ publisher = {Springer}, doi = {10.1007/s10957-021-01896-x}, url = {https://doi.org/10.1007/s10957-021-01896-x} -}

    The article is available under Open Access here.

    Contributing

    • Contributions are always welcome. Our style guide can be found here.
    • Current issues, tasks and future ideas are listed in Issues. Please report any issues or bugs that you encounter.
    • As an open source project we are also interested in any projects and applications that use COSMO. Please let us know by opening a GitHub issue.

    Python - Interface

    COSMO can also be called from Python. Take a look at: cosmo-python

    Licence 🔍

    This project is licensed under the Apache License - see the LICENSE.md file for details.

    +}

    The article is available under Open Access here.

    Contributing

    • Contributions are always welcome. Our style guide can be found here.
    • Current issues, tasks and future ideas are listed in Issues. Please report any issues or bugs that you encounter.
    • As an open source project we are also interested in any projects and applications that use COSMO. Please let us know by opening a GitHub issue.

    Python - Interface

    COSMO can also be called from Python. Take a look at: cosmo-python

    Licence 🔍

    This project is licensed under the Apache License - see the LICENSE.md file for details.

    diff --git a/previews/PR3913/packages/CPLEX/index.html b/previews/PR3913/packages/CPLEX/index.html index 7e6e192e837..9605546ee49 100644 --- a/previews/PR3913/packages/CPLEX/index.html +++ b/previews/PR3913/packages/CPLEX/index.html @@ -163,4 +163,4 @@ x_optimal = value.(x) y_optimal = value.(y) println("x: $(x_optimal), y: $(y_optimal)") -end +end diff --git a/previews/PR3913/packages/CSDP/index.html b/previews/PR3913/packages/CSDP/index.html index 9ee692e6d94..a32652de5e0 100644 --- a/previews/PR3913/packages/CSDP/index.html +++ b/previews/PR3913/packages/CSDP/index.html @@ -10,4 +10,4 @@ A(X) = a X ⪰ 0

    where A(X) = [⟨A_1, X⟩, ..., ⟨A_m, X⟩]. The corresponding dual is:

    min ⟨a, y⟩
      A'(y) - C = Z
-             Z ⪰ 0

    where A'(y) = y_1A_1 + ... + y_mA_m

    Termination criteria

    CSDP will terminate successfully (or partially) in the following cases:

    • If CSDP finds X, Z ⪰ 0 such that the following 3 tolerances are satisfied:
      • primal feasibility tolerance: ||A(x) - a||_2 / (1 + ||a||_2) < axtol
      • dual feasibility tolerance: ||A'(y) - C - Z||_F / (1 + ||C||_F) < atytol
      • relative duality gap tolerance: gap / (1 + |⟨a, y⟩| + |⟨C, X⟩|) < objtol
        • objective duality gap: if usexygap is 0, gap = ⟨a, y⟩ - ⟨C, X⟩
        • XY duality gap: if usexygap is 1, gap = ⟨Z, X⟩
      then it returns 0.
    • If CSDP finds y and Z ⪰ 0 such that -⟨a, y⟩ / ||A'(y) - Z||_F > pinftol, it returns 1 with y such that ⟨a, y⟩ = -1.
    • If CSDP finds X ⪰ 0 such that ⟨C, X⟩ / ||A(X)||_2 > dinftol, it returns 2 with X such that ⟨C, X⟩ = 1.
    • If CSDP finds X, Z ⪰ 0 such that the following 3 tolerances are satisfied with 1000*axtol, 1000*atytol and 1000*objtol but at least one of them is not satisfied with axtol, atytol and objtol and cannot make progress, then it returns 3.

    In addition, if the printlevel option is at least 1, the following will be printed:

    • If the return code is 1, CSDP will print ⟨a, y⟩ and ||A'(y) - Z||_F
    • If the return code is 2, CSDP will print ⟨C, X⟩ and ||A(X)||_F
    • Otherwise, CSDP will print
      • the primal/dual objective value,
      • the relative primal/dual infeasibility,
      • the objective duality gap ⟨a, y⟩ - ⟨C, X⟩ and objective relative duality gap (⟨a, y⟩ - ⟨C, X⟩) / (1 + |⟨a, y⟩| + |⟨C, X⟩|),
      • the XY duality gap ⟨Z, X⟩ and XY relative duality gap ⟨Z, X⟩ / (1 + |⟨a, y⟩| + |⟨C, X⟩|)
      • and the DIMACS error measures.

    In theory, for feasible primal and dual solutions, ⟨a, y⟩ - ⟨C, X⟩ = ⟨Z, X⟩, so the objective and XY duality gap should be equivalent. However, in practice, there are sometimes solution which satisfy primal and dual feasibility tolerances but have objective duality gap which are not close to XY duality gap. In some cases, the objective duality gap may even become negative (hence the tweakgap option). This is the reason usexygap is 1 by default.

    CSDP considers that X ⪰ 0 (resp. Z ⪰ 0) is satisfied when the Cholesky factorizations can be computed. In practice, this is somewhat more conservative than simply requiring all eigenvalues to be nonnegative.

    Status

    The table below shows how the different CSDP statuses are converted to the MathOptInterface statuses.

    CSDP codeStateDescriptionMOI status
    0SuccessSDP solvedMOI.OPTIMAL
    1SuccessThe problem is primal infeasible, and we have a certificateMOI.INFEASIBLE
    2SuccessThe problem is dual infeasible, and we have a certificateMOI.DUAL_INFEASIBLE
    3Partial SuccessA solution has been found, but full accuracy was not achievedMOI.ALMOST_OPTIMAL
    4FailureMaximum iterations reachedMOI.ITERATION_LIMIT
    5FailureStuck at edge of primal feasibilityMOI.SLOW_PROGRESS
    6FailureStuck at edge of dual infeasibilityMOI.SLOW_PROGRESS
    7FailureLack of progressMOI.SLOW_PROGRESS
    8FailureX, Z, or O was singularMOI.NUMERICAL_ERROR
    9FailureDetected NaN or Inf valuesMOI.NUMERICAL_ERROR
    + Z ⪰ 0

    where A'(y) = y_1A_1 + ... + y_mA_m

    Termination criteria

    CSDP will terminate successfully (or partially) in the following cases:

    • If CSDP finds X, Z ⪰ 0 such that the following 3 tolerances are satisfied:
      • primal feasibility tolerance: ||A(x) - a||_2 / (1 + ||a||_2) < axtol
      • dual feasibility tolerance: ||A'(y) - C - Z||_F / (1 + ||C||_F) < atytol
      • relative duality gap tolerance: gap / (1 + |⟨a, y⟩| + |⟨C, X⟩|) < objtol
        • objective duality gap: if usexygap is 0, gap = ⟨a, y⟩ - ⟨C, X⟩
        • XY duality gap: if usexygap is 1, gap = ⟨Z, X⟩
      then it returns 0.
    • If CSDP finds y and Z ⪰ 0 such that -⟨a, y⟩ / ||A'(y) - Z||_F > pinftol, it returns 1 with y such that ⟨a, y⟩ = -1.
    • If CSDP finds X ⪰ 0 such that ⟨C, X⟩ / ||A(X)||_2 > dinftol, it returns 2 with X such that ⟨C, X⟩ = 1.
    • If CSDP finds X, Z ⪰ 0 such that the following 3 tolerances are satisfied with 1000*axtol, 1000*atytol and 1000*objtol but at least one of them is not satisfied with axtol, atytol and objtol and cannot make progress, then it returns 3.

    In addition, if the printlevel option is at least 1, the following will be printed:

    • If the return code is 1, CSDP will print ⟨a, y⟩ and ||A'(y) - Z||_F
    • If the return code is 2, CSDP will print ⟨C, X⟩ and ||A(X)||_F
    • Otherwise, CSDP will print
      • the primal/dual objective value,
      • the relative primal/dual infeasibility,
      • the objective duality gap ⟨a, y⟩ - ⟨C, X⟩ and objective relative duality gap (⟨a, y⟩ - ⟨C, X⟩) / (1 + |⟨a, y⟩| + |⟨C, X⟩|),
      • the XY duality gap ⟨Z, X⟩ and XY relative duality gap ⟨Z, X⟩ / (1 + |⟨a, y⟩| + |⟨C, X⟩|)
      • and the DIMACS error measures.

    In theory, for feasible primal and dual solutions, ⟨a, y⟩ - ⟨C, X⟩ = ⟨Z, X⟩, so the objective and XY duality gap should be equivalent. However, in practice, there are sometimes solution which satisfy primal and dual feasibility tolerances but have objective duality gap which are not close to XY duality gap. In some cases, the objective duality gap may even become negative (hence the tweakgap option). This is the reason usexygap is 1 by default.

    CSDP considers that X ⪰ 0 (resp. Z ⪰ 0) is satisfied when the Cholesky factorizations can be computed. In practice, this is somewhat more conservative than simply requiring all eigenvalues to be nonnegative.

    Status

    The table below shows how the different CSDP statuses are converted to the MathOptInterface statuses.

    CSDP codeStateDescriptionMOI status
    0SuccessSDP solvedMOI.OPTIMAL
    1SuccessThe problem is primal infeasible, and we have a certificateMOI.INFEASIBLE
    2SuccessThe problem is dual infeasible, and we have a certificateMOI.DUAL_INFEASIBLE
    3Partial SuccessA solution has been found, but full accuracy was not achievedMOI.ALMOST_OPTIMAL
    4FailureMaximum iterations reachedMOI.ITERATION_LIMIT
    5FailureStuck at edge of primal feasibilityMOI.SLOW_PROGRESS
    6FailureStuck at edge of dual infeasibilityMOI.SLOW_PROGRESS
    7FailureLack of progressMOI.SLOW_PROGRESS
    8FailureX, Z, or O was singularMOI.NUMERICAL_ERROR
    9FailureDetected NaN or Inf valuesMOI.NUMERICAL_ERROR
    diff --git a/previews/PR3913/packages/Cbc/index.html b/previews/PR3913/packages/Cbc/index.html index f4c1c6951a5..8663f86a5fe 100644 --- a/previews/PR3913/packages/Cbc/index.html +++ b/previews/PR3913/packages/Cbc/index.html @@ -9,4 +9,4 @@ set_attribute(model, "logLevel", 1)

    MathOptInterface API

    The COIN Branch-and-Cut (Cbc) optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    List of supported optimizer attributes:

    List of supported variable attributes:

    List of supported constraint attributes:

    Options

    Options are, unfortunately, not well documented.

    The following options are likely to be the most useful:

    ParameterExampleExplanation
    seconds60.0Solution timeout limit
    logLevel2Set to 0 to disable solution output
    maxSolutions1Terminate after this many feasible solutions have been found
    maxNodes1Terminate after this many branch-and-bound nodes have been evaluated
    allowableGap0.05Terminate after optimality gap is less than this value (on an absolute scale)
    ratioGap0.05Terminate after optimality gap is smaller than this relative fraction
    threads1Set the number of threads to use for parallel branch & bound

    The complete list of parameters can be found by running the cbc executable and typing ? at the prompt.

    Start the cbc executable from Julia as follows:

    using Cbc_jll
 Cbc_jll.cbc() do exe
     run(`$(exe)`)
-end
    +end diff --git a/previews/PR3913/packages/Clarabel/index.html b/previews/PR3913/packages/Clarabel/index.html index be3517fb858..2b49a8af07a 100644 --- a/previews/PR3913/packages/Clarabel/index.html +++ b/previews/PR3913/packages/Clarabel/index.html @@ -33,4 +33,4 @@

    eprint={2405.12762}, archivePrefix={arXiv}, primaryClass={math.OC} -}

    License 🔍

    This project is licensed under the Apache License 2.0 - see the LICENSE.md file for details.

    +}

    License 🔍

    This project is licensed under the Apache License 2.0 - see the LICENSE.md file for details.

    diff --git a/previews/PR3913/packages/Clp/index.html b/previews/PR3913/packages/Clp/index.html index a14bc10c599..bfb949b2192 100644 --- a/previews/PR3913/packages/Clp/index.html +++ b/previews/PR3913/packages/Clp/index.html @@ -7,4 +7,4 @@ Pkg.add("Clp")

    In addition to installing the Clp.jl package, this will also download and install the Clp binaries. You do not need to install Clp separately.

    To use a custom binary, read the Custom solver binaries section of the JuMP documentation.

    Use with JuMP

    To use Clp with JuMP, use Clp.Optimizer:

    using JuMP, Clp
 model = Model(Clp.Optimizer)
 set_attribute(model, "LogLevel", 1)
-set_attribute(model, "Algorithm", 4)

    MathOptInterface API

    The Clp optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    Options are, unfortunately, not well documented.

    The following options are likely to be the most useful:

    ParameterExampleExplanation
    PrimalTolerance1e-7Primal feasibility tolerance
    DualTolerance1e-7Dual feasibility tolerance
    DualObjectiveLimit1e308When using dual simplex (where the objective is monotonically changing), terminate when the objective exceeds this limit
    MaximumIterations2147483647Terminate after performing this number of simplex iterations
    MaximumSeconds-1.0Terminate after this many seconds have passed. A negative value means no time limit
    LogLevel1Set to 1, 2, 3, or 4 for increasing output. Set to 0 to disable output
    PresolveType0Set to 1 to disable presolve
    SolveType5Solution method: dual simplex (0), primal simplex (1), sprint (2), barrier with crossover (3), barrier without crossover (4), automatic (5)
    InfeasibleReturn0Set to 1 to return as soon as the problem is found to be infeasible (by default, an infeasibility proof is computed as well)
    Scaling30 -off, 1 equilibrium, 2 geometric, 3 auto, 4 dynamic(later)
    Perturbation100switch on perturbation (50), automatic (100), don't try perturbing (102)

    C API

    The C API can be accessed via Clp.Clp_XXX functions, where the names and arguments are identical to the C API.

    +set_attribute(model, "Algorithm", 4)

    MathOptInterface API

    The Clp optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    Options are, unfortunately, not well documented.

    The following options are likely to be the most useful:

    ParameterExampleExplanation
    PrimalTolerance1e-7Primal feasibility tolerance
    DualTolerance1e-7Dual feasibility tolerance
    DualObjectiveLimit1e308When using dual simplex (where the objective is monotonically changing), terminate when the objective exceeds this limit
    MaximumIterations2147483647Terminate after performing this number of simplex iterations
    MaximumSeconds-1.0Terminate after this many seconds have passed. A negative value means no time limit
    LogLevel1Set to 1, 2, 3, or 4 for increasing output. Set to 0 to disable output
    PresolveType0Set to 1 to disable presolve
    SolveType5Solution method: dual simplex (0), primal simplex (1), sprint (2), barrier with crossover (3), barrier without crossover (4), automatic (5)
    InfeasibleReturn0Set to 1 to return as soon as the problem is found to be infeasible (by default, an infeasibility proof is computed as well)
    Scaling30 -off, 1 equilibrium, 2 geometric, 3 auto, 4 dynamic(later)
    Perturbation100switch on perturbation (50), automatic (100), don't try perturbing (102)

    C API

    The C API can be accessed via Clp.Clp_XXX functions, where the names and arguments are identical to the C API.

    diff --git a/previews/PR3913/packages/DAQP/index.html b/previews/PR3913/packages/DAQP/index.html index afe9b49646a..b51ad7bbf80 100644 --- a/previews/PR3913/packages/DAQP/index.html +++ b/previews/PR3913/packages/DAQP/index.html @@ -5,4 +5,4 @@ gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash});
    GitHub

    DAQP.jl

    DAQP.jl is a Julia wrapper for the Quadratic Programming solver DAQP.

    License

    DAQP.jl is licensed under the MIT license.

    The underlying solver, darnstrom/daqp is licensed under the MIT license.

    Installation

    Install DAQP.jl using the Julia package manager:

    import Pkg
 Pkg.add("DAQP")

    Use with JuMP

    To use DAQP with JuMP, do:

    using JuMP, DAQP
-model = Model(DAQP.Optimizer)

    Documentation

    General information about the solver is available at https://darnstrom.github.io/daqp/, and specifics for the Julia interface are available at https://darnstrom.github.io/daqp/start/julia.

    +model = Model(DAQP.Optimizer)

    Documentation

    General information about the solver is available at https://darnstrom.github.io/daqp/, and specifics for the Julia interface are available at https://darnstrom.github.io/daqp/start/julia.

    diff --git a/previews/PR3913/packages/DSDP/index.html b/previews/PR3913/packages/DSDP/index.html index e345e98244f..4f9c3ff12ad 100644 --- a/previews/PR3913/packages/DSDP/index.html +++ b/previews/PR3913/packages/DSDP/index.html @@ -8,4 +8,4 @@ model = Model(DSDP.Optimizer)

    MathOptInterface API

    The DSDP optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Compile your own binaries

    In order to compile your own libdsdp.so to be used of DSDP.jl, use the following

    OB_DIR=$(julia --project=. -e 'import OpenBLAS32_jll; println(OpenBLAS32_jll.OpenBLAS32_jll.artifact_dir)')
 OB="-L${LIBOB_DIR}/lib -lopenblas"
 make DSDPCFLAGS="-g -Wall -fPIC -DPIC" LAPACKBLAS="$OB" dsdplibrary
-make DSDPCFLAGS="-g -Wall -fPIC -DPIC" LAPACKBLAS="$OB" SH_LD="${CC} ${CFLAGS} -Wall -fPIC -DPIC -shared $OB" oshared
    +make DSDPCFLAGS="-g -Wall -fPIC -DPIC" LAPACKBLAS="$OB" SH_LD="${CC} ${CFLAGS} -Wall -fPIC -DPIC -shared $OB" oshared diff --git a/previews/PR3913/packages/DiffOpt/index.html b/previews/PR3913/packages/DiffOpt/index.html index 008fb5ae82a..9ac05557f8a 100644 --- a/previews/PR3913/packages/DiffOpt/index.html +++ b/previews/PR3913/packages/DiffOpt/index.html @@ -20,4 +20,4 @@ # fetch the gradients grad_exp = MOI.get(model, DiffOpt.ReverseConstraintFunction(), cons) # -3 x - 1 constant(grad_exp) # -1 -coefficient(grad_exp, x) # -3

    GSOC2020

    DiffOpt began as a NumFOCUS sponsored Google Summer of Code (2020) project

    +coefficient(grad_exp, x) # -3

    GSOC2020

    DiffOpt began as a NumFOCUS sponsored Google Summer of Code (2020) project

    diff --git a/previews/PR3913/packages/DisjunctiveProgramming/index.html b/previews/PR3913/packages/DisjunctiveProgramming/index.html index 7458c8aa139..ae4e4ddabb8 100644 --- a/previews/PR3913/packages/DisjunctiveProgramming/index.html +++ b/previews/PR3913/packages/DisjunctiveProgramming/index.html @@ -8,4 +8,4 @@ author={Perez, Hector D and Joshi, Shivank and Grossmann, Ignacio E}, journal={arXiv preprint arXiv:2304.10492}, year={2023} -} +} diff --git a/previews/PR3913/packages/Dualization/index.html b/previews/PR3913/packages/Dualization/index.html index c8cab0acc1b..9a38259b4d2 100644 --- a/previews/PR3913/packages/Dualization/index.html +++ b/previews/PR3913/packages/Dualization/index.html @@ -10,4 +10,4 @@ dual_model = dualize(model)

    To solve the dual formulation of a JuMP model, create a dual_optimizer:

    using JuMP, Dualization, SCS
 model = Model(dual_optimizer(SCS.Optimizer))
 # ... build model ...
-optimize!(model)  # Solves the dual instead of the primal

    Documentation

    The documentation for Dualization.jl includes a detailed description of the dual reformulation, along with examples and an API reference.

    +optimize!(model) # Solves the dual instead of the primal

    Documentation

    The documentation for Dualization.jl includes a detailed description of the dual reformulation, along with examples and an API reference.

    diff --git a/previews/PR3913/packages/EAGO/index.html b/previews/PR3913/packages/EAGO/index.html index d60b0ad0b11..6c46ed4b51a 100644 --- a/previews/PR3913/packages/EAGO/index.html +++ b/previews/PR3913/packages/EAGO/index.html @@ -71,4 +71,4 @@ doi = {10.1080/10556788.2020.1786566}, URL = {https://doi.org/10.1080/10556788.2020.1786566}, eprint = {https://doi.org/10.1080/10556788.2020.1786566} -}

    References

    1. Mitsos, A., Chachuat, B., and Barton, P.I. McCormick-based relaxations of algorithms. SIAM Journal on Optimization. 20(2): 573—601 (2009).
    2. Khan, K.A., Watson, H.A.J., and Barton, P.I. Differentiable McCormick relaxations. Journal of Global Optimization. 67(4): 687—729 (2017).
    3. Stuber, M.D., Scott, J.K., and Barton, P.I.: Convex and concave relaxations of implicit functions. Optimization Methods and Software 30(3): 424—460 (2015).
    4. Wechsung, A., Scott, J.K., Watson, H.A.J., and Barton, P.I. Reverse propagation of McCormick relaxations. Journal of Global Optimization 63(1): 1—36 (2015).
    5. Bracken, J., and McCormick, G.P. Selected Applications of Nonlinear Programming. John Wiley and Sons, New York (1968).
    +}

    References

    1. Mitsos, A., Chachuat, B., and Barton, P.I. McCormick-based relaxations of algorithms. SIAM Journal on Optimization. 20(2): 573—601 (2009).
    2. Khan, K.A., Watson, H.A.J., and Barton, P.I. Differentiable McCormick relaxations. Journal of Global Optimization. 67(4): 687—729 (2017).
    3. Stuber, M.D., Scott, J.K., and Barton, P.I.: Convex and concave relaxations of implicit functions. Optimization Methods and Software 30(3): 424—460 (2015).
    4. Wechsung, A., Scott, J.K., Watson, H.A.J., and Barton, P.I. Reverse propagation of McCormick relaxations. Journal of Global Optimization 63(1): 1—36 (2015).
    5. Bracken, J., and McCormick, G.P. Selected Applications of Nonlinear Programming. John Wiley and Sons, New York (1968).
    diff --git a/previews/PR3913/packages/ECOS/index.html b/previews/PR3913/packages/ECOS/index.html index d2106001885..0816afb8707 100644 --- a/previews/PR3913/packages/ECOS/index.html +++ b/previews/PR3913/packages/ECOS/index.html @@ -6,4 +6,4 @@
    GitHub

    ECOS.jl

    Build Status codecov

    ECOS.jl is a wrapper for the ECOS solver.

    The wrapper has two components:

    Affiliation

    This wrapper is maintained by the JuMP community and is not a product of Embotech AG.

    License

    ECOS.jl is licensed under the MIT License.

    The underlying solver, embotech/ecos, is licensed under the GPL v3 license.

    Installation

    Install ECOS.jl using Pkg.add:

    import Pkg
 Pkg.add("ECOS")

    In addition to installing the ECOS.jl package, this will also download and install the ECOS binaries. You do not need to install ECOS separately.

    To use a custom binary, read the Custom solver binaries section of the JuMP documentation.

    Use with JuMP

    To use ECOS with JuMP, use ECOS.Optimizer:

    using JuMP, ECOS
 model = Model(ECOS.Optimizer)
-set_attribute(model, "maxit", 100)

    MathOptInterface API

    The ECOS optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    The following options are supported:

    ParameterExplanation
    gammascaling the final step length
    deltaregularization parameter
    epsregularization threshold
    feastolprimal/dual infeasibility tolerance
    abstolabsolute tolerance on duality gap
    reltolrelative tolerance on duality gap
    feastol_inaccprimal/dual infeasibility relaxed tolerance
    abstol_inaccabsolute relaxed tolerance on duality gap
    reltol_inaccrelative relaxed tolerance on duality gap
    nitrefnumber of iterative refinement steps
    maxitmaximum number of iterations
    verboseverbosity bool for PRINTLEVEL < 3
    +set_attribute(model, "maxit", 100)

    MathOptInterface API

    The ECOS optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    The following options are supported:

    ParameterExplanation
    gammascaling the final step length
    deltaregularization parameter
    epsregularization threshold
    feastolprimal/dual infeasibility tolerance
    abstolabsolute tolerance on duality gap
    reltolrelative tolerance on duality gap
    feastol_inaccprimal/dual infeasibility relaxed tolerance
    abstol_inaccabsolute relaxed tolerance on duality gap
    reltol_inaccrelative relaxed tolerance on duality gap
    nitrefnumber of iterative refinement steps
    maxitmaximum number of iterations
    verboseverbosity bool for PRINTLEVEL < 3
    diff --git a/previews/PR3913/packages/GAMS/index.html b/previews/PR3913/packages/GAMS/index.html index 618f8ef2bcb..387d708ed9e 100644 --- a/previews/PR3913/packages/GAMS/index.html +++ b/previews/PR3913/packages/GAMS/index.html @@ -22,4 +22,4 @@ MOI.get(model, GAMS.GeneratedConstraintName(), c[2]) # returns eq2 MOI.get(model, GAMS.OriginalConstraintName("eq1")) # returns c[1] -MOI.get(model, GAMS.OriginalConstraintName("eq10")) # returns nothing

    Note that JuMP direct-mode is used.

    +MOI.get(model, GAMS.OriginalConstraintName("eq10")) # returns nothing

    Note that JuMP direct-mode is used.

    diff --git a/previews/PR3913/packages/GLPK/index.html b/previews/PR3913/packages/GLPK/index.html index 3e29faf6b6d..c78eb58b432 100644 --- a/previews/PR3913/packages/GLPK/index.html +++ b/previews/PR3913/packages/GLPK/index.html @@ -36,4 +36,4 @@ @test primal_status(model) == MOI.FEASIBLE_POINT @test value(x) == 1 @test value(y) == 2 -@show reasons

    C API

    The C API can be accessed via GLPK.glp_XXX functions, where the names and arguments are identical to the C API. See the /tests folder for inspiration.

    Thread safety

    GLPK is not thread-safe and should not be used with multithreading.

    +@show reasons

    C API

    The C API can be accessed via GLPK.glp_XXX functions, where the names and arguments are identical to the C API. See the /tests folder for inspiration.

    Thread safety

    GLPK is not thread-safe and should not be used with multithreading.

    diff --git a/previews/PR3913/packages/Gurobi/index.html b/previews/PR3913/packages/Gurobi/index.html index c8bdf9a70ce..b986d91e8bf 100644 --- a/previews/PR3913/packages/Gurobi/index.html +++ b/previews/PR3913/packages/Gurobi/index.html @@ -175,4 +175,4 @@ println(lower_bound(x[i])) end

    Common errors

    Using Gurobi v9.0 and you got an error like Q not PSD?

    You need to set the NonConvex parameter:

    model = Model(Gurobi.Optimizer)
 set_optimizer_attribute(model, "NonConvex", 2)

    Gurobi Error 1009: Version number is XX.X, license is for version XX.X

    Make sure that your license is correct for your Gurobi version. See the Gurobi documentation for details.

    Once you are sure that the license and Gurobi versions match, re-install Gurobi.jl by running:

    import Pkg
-Pkg.build("Gurobi")
    +Pkg.build("Gurobi") diff --git a/previews/PR3913/packages/HiGHS/index.html b/previews/PR3913/packages/HiGHS/index.html index 7686bb59820..8c63e41ac88 100644 --- a/previews/PR3913/packages/HiGHS/index.html +++ b/previews/PR3913/packages/HiGHS/index.html @@ -11,4 +11,4 @@ set_attribute(model, "time_limit", 60.0)

    MathOptInterface API

    The HiGHS optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    See the HiGHS documentation for a full list of the available options.

    C API

    The C API can be accessed via HiGHS.Highs_xxx functions, where the names and arguments are identical to the C API.

    Threads

    HiGHS uses a global scheduler that is shared between threads.

    Before changing the number of threads using MOI.Threads(), you must call Highs_resetGlobalScheduler(1):

    using JuMP, HiGHS
 model = Model(HiGHS.Optimizer)
 Highs_resetGlobalScheduler(1)
-set_attribute(model, MOI.NumberOfThreads(), 1)

    If modifying the number of HiGHS threads across different Julia threads, be sure to read the docstring of Highs_resetGlobalScheduler. In particular, resetting the scheduler is not thread-safe.

    +set_attribute(model, MOI.NumberOfThreads(), 1)

    If modifying the number of HiGHS threads across different Julia threads, be sure to read the docstring of Highs_resetGlobalScheduler. In particular, resetting the scheduler is not thread-safe.

    diff --git a/previews/PR3913/packages/Hypatia/index.html b/previews/PR3913/packages/Hypatia/index.html index 72617fea7a3..711fc1c6739 100644 --- a/previews/PR3913/packages/Hypatia/index.html +++ b/previews/PR3913/packages/Hypatia/index.html @@ -42,4 +42,4 @@ volume={15}, pages={53--101}, doi={https://doi.org/10.1007/s12532-022-00226-0} -} +} diff --git a/previews/PR3913/packages/InfiniteOpt/index.html b/previews/PR3913/packages/InfiniteOpt/index.html index 67e843b3b8f..6bb8dd3f6f1 100644 --- a/previews/PR3913/packages/InfiniteOpt/index.html +++ b/previews/PR3913/packages/InfiniteOpt/index.html @@ -12,4 +12,4 @@ doi = {https://doi.org/10.1016/j.compchemeng.2021.107567}, url = {https://www.sciencedirect.com/science/article/pii/S0098135421003458}, author = {Joshua L. Pulsipher and Weiqi Zhang and Tyler J. Hongisto and Victor M. Zavala}, -}

    A pre-print version is freely available though arXiv.

    +}

    A pre-print version is freely available though arXiv.

    diff --git a/previews/PR3913/packages/Ipopt/index.html b/previews/PR3913/packages/Ipopt/index.html index bf798337417..3327d37da00 100644 --- a/previews/PR3913/packages/Ipopt/index.html +++ b/previews/PR3913/packages/Ipopt/index.html @@ -124,4 +124,4 @@ LinearAlgebra.BLAS.lbt_forward(liblapack32) using Ipopt

    AppleAccelerate

    If you are using macOS ≥ v13.4 and you have AppleAccelerate.jl installed, add using AppleAccelerate to your code:

    using AppleAccelerate
 using Ipopt

    Display backends

    Check what backends are loaded using:

    import LinearAlgebra
-LinearAlgebra.BLAS.lbt_get_config()
    +LinearAlgebra.BLAS.lbt_get_config() diff --git a/previews/PR3913/packages/Juniper/index.html b/previews/PR3913/packages/Juniper/index.html index 5e34b370295..8554bcc81c9 100644 --- a/previews/PR3913/packages/Juniper/index.html +++ b/previews/PR3913/packages/Juniper/index.html @@ -33,4 +33,4 @@ year="2018", publisher="Springer International Publishing", isbn="978-3-319-93031-2" -} +} diff --git a/previews/PR3913/packages/KNITRO/index.html b/previews/PR3913/packages/KNITRO/index.html index 300c67bde49..a7b080fc706 100644 --- a/previews/PR3913/packages/KNITRO/index.html +++ b/previews/PR3913/packages/KNITRO/index.html @@ -10,4 +10,4 @@ set_attribute(model, "algorithm", 4)

    Use with AMPL

    To use KNITRO with AmplNLWriter.jl, use KNITRO.amplexe:

    using JuMP
 import AmplNLWriter
 import KNITRO
-model = Model(() -> AmplNLWriter.Optimizer(KNITRO.amplexe, ["outlev=3"]))

    Use with other packages

    A variety of packages extend KNITRO.jl to support other optimization modeling systems. These include:

    MathOptInterface API

    The Knitro optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    A list of available options is provided in the KNITRO reference manual.

    Low-level wrapper

    The complete C API can be accessed via KNITRO.KN_xx functions, where the names and arguments are identical to the C API.

    See the KNITRO documentation for details.

    As general rules when converting from Julia to C:

    • When KNITRO requires a Ptr{T} that holds one element, like double *, use a Ref{T}().
    • When KNITRO requires a Ptr{T} that holds multiple elements, use a Vector{T}.
    • When KNITRO requires a double, use Cdouble
    • When KNITRO requires an int, use Cint
    • When KNITRO requires a NULL, use C_NULL

    Extensive examples using the C wrapper can be found in examples/.

    Breaking changes

    KNITRO.jl v0.14.0 introduced a number of breaking changes to the low-level C API. The main changes were:

    1. removing Julia-specific functions like KN_set_param. Use the C API functions like KN_set_int_param and KN_set_double_param_by_name.
    2. removing intermediate methods that tried to make the C API more Julia-like. For example, we have removed the KN_add_var method that returned the index of the variable. There is now only the method from the C API.

    If you have trouble updating, please open a GitHub issue.

    Multi-threading

    Due to limitations in the interaction between Julia and C, KNITRO.jl disables multi-threading if the problem is nonlinear. This will override any options such as par_numthreads that you may have set.

    If you are using the low-level API, opt-in to enable multi-threading by calling KN_solve(model.env) instead of KN_solve(model), where model is the value returned by model = KN_new(). Note that calling KN_solve(model.env) is an advanced operation because it requires all callbacks you provide to be threadsafe.

    Read GitHub issue #93 for more details.

    +model = Model(() -> AmplNLWriter.Optimizer(KNITRO.amplexe, ["outlev=3"]))

    Use with other packages

    A variety of packages extend KNITRO.jl to support other optimization modeling systems. These include:

    MathOptInterface API

    The Knitro optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    A list of available options is provided in the KNITRO reference manual.

    Low-level wrapper

    The complete C API can be accessed via KNITRO.KN_xx functions, where the names and arguments are identical to the C API.

    See the KNITRO documentation for details.

    As general rules when converting from Julia to C:

    • When KNITRO requires a Ptr{T} that holds one element, like double *, use a Ref{T}().
    • When KNITRO requires a Ptr{T} that holds multiple elements, use a Vector{T}.
    • When KNITRO requires a double, use Cdouble
    • When KNITRO requires an int, use Cint
    • When KNITRO requires a NULL, use C_NULL

    Extensive examples using the C wrapper can be found in examples/.

    Breaking changes

    KNITRO.jl v0.14.0 introduced a number of breaking changes to the low-level C API. The main changes were:

    1. removing Julia-specific functions like KN_set_param. Use the C API functions like KN_set_int_param and KN_set_double_param_by_name.
    2. removing intermediate methods that tried to make the C API more Julia-like. For example, we have removed the KN_add_var method that returned the index of the variable. There is now only the method from the C API.

    If you have trouble updating, please open a GitHub issue.

    Multi-threading

    Due to limitations in the interaction between Julia and C, KNITRO.jl disables multi-threading if the problem is nonlinear. This will override any options such as par_numthreads that you may have set.

    If you are using the low-level API, opt-in to enable multi-threading by calling KN_solve(model.env) instead of KN_solve(model), where model is the value returned by model = KN_new(). Note that calling KN_solve(model.env) is an advanced operation because it requires all callbacks you provide to be threadsafe.

    Read GitHub issue #93 for more details.

    diff --git a/previews/PR3913/packages/Loraine/index.html b/previews/PR3913/packages/Loraine/index.html index 8343706af12..cf0e85c3700 100644 --- a/previews/PR3913/packages/Loraine/index.html +++ b/previews/PR3913/packages/Loraine/index.html @@ -37,4 +37,4 @@ www={https://hal.science/hal-04076509/} note={Preprint hal-04076509} year={2023} -}
    • 1https://www.youtube.com/watch?v=0D2wNf1lVrI
    +}
    • 1https://www.youtube.com/watch?v=0D2wNf1lVrI
    diff --git a/previews/PR3913/packages/MAiNGO/index.html b/previews/PR3913/packages/MAiNGO/index.html index 019e16e508a..bb4d90c7442 100644 --- a/previews/PR3913/packages/MAiNGO/index.html +++ b/previews/PR3913/packages/MAiNGO/index.html @@ -94,4 +94,4 @@ findMAiNGO(preferred=MAiNGO.C_API) # switch back to MAiNGO_jll findMAiNGO(preferred=MAiNGO.MAINGO_JLL)

    The findMAiNGO() function takes several optional arguments, which can be passed as keyword-arguments:

    • verbose: boolean, whether or not progress on finding MAiNGO is reported. (Default value: false)
    • preferred: either MAiNGO.MAINGOJLL or MAiNGO.CAPI, determines whether jll binaries or custom installation of MAiNGO is preferred. Note that the C-API is always preferred to the standalone version. If a custom standalone version should be used, set this value to C-API and pass an empty string as the capi argument (see next). (Default value: MAINGOJLL)
    • capi: string, path to C-API file. If set, this overrides the environment variable MAINGOLIB.
    • standalone: string, path to standalone executable file. If set, this overrides the environment variable MAINGO_EXEC.

    For example, to use the C-API at a new location, one could call:

    using MAiNGO
-findMAiNGO(preferred=MAiNGO.C_API, c_api="path\\to\\c\\api\\shared_parser.dll")

    Currently working:

    • Integer and binary variables.
    • Affine, Quadratic and nonlinear constraints and objectives.
    • Operations: min,max,*,/,+,-,-(unary), exp,log,abs,sqrt,^
      • Other operations are easy to add if supported by MathOptInterface,ALE and MAiNGO.
    • Writing problem defined in JuMP syntax to an ALE problem.txt and calling MAiNGO.exe on a specified path.
    • Alternatively using a C-API to call MAiNGO.

    Restrictions compared to using the Python or C++ interface

    It is assumed that all variables are bounded. This interface assumes that integer variables are bounded between -1e6 and 1e6. For real variables these bounds are -1e8 and 1e8.

    Other functionality such as special support for growing datasets or MPI parallelization is not currently supported via this wrapper. Additionally, constraint formulations are simply passed from their representation in JuMP/MathOptInterface to MAiNGO. As such, there is no way to make use of advanced techniques such as defining constraints that are only used for the relaxations, using special relaxations for functions used in thermodynamics and process engineering or formulating reduced space formulations.

    Tests

    A subset of test cases for MathOptInterface solvers can be run by running the script ./test/runtests.jl. The current release was tested in the following combinations:

    • Julia 1.8.5 and MathOptInterface v1.18.0
    • Julia 1.9.4 and MathOptInterface v1.23.0.
    +findMAiNGO(preferred=MAiNGO.C_API, c_api="path\\to\\c\\api\\shared_parser.dll")

    Currently working:

    • Integer and binary variables.
    • Affine, Quadratic and nonlinear constraints and objectives.
    • Operations: min,max,*,/,+,-,-(unary), exp,log,abs,sqrt,^
      • Other operations are easy to add if supported by MathOptInterface,ALE and MAiNGO.
    • Writing problem defined in JuMP syntax to an ALE problem.txt and calling MAiNGO.exe on a specified path.
    • Alternatively using a C-API to call MAiNGO.

    Restrictions compared to using the Python or C++ interface

    It is assumed that all variables are bounded. This interface assumes that integer variables are bounded between -1e6 and 1e6. For real variables these bounds are -1e8 and 1e8.

    Other functionality such as special support for growing datasets or MPI parallelization is not currently supported via this wrapper. Additionally, constraint formulations are simply passed from their representation in JuMP/MathOptInterface to MAiNGO. As such, there is no way to make use of advanced techniques such as defining constraints that are only used for the relaxations, using special relaxations for functions used in thermodynamics and process engineering or formulating reduced space formulations.

    Tests

    A subset of test cases for MathOptInterface solvers can be run by running the script ./test/runtests.jl. The current release was tested in the following combinations:

    • Julia 1.8.5 and MathOptInterface v1.18.0
    • Julia 1.9.4 and MathOptInterface v1.23.0.
    diff --git a/previews/PR3913/packages/MadNLP/index.html b/previews/PR3913/packages/MadNLP/index.html index 148ea830869..00910035e50 100644 --- a/previews/PR3913/packages/MadNLP/index.html +++ b/previews/PR3913/packages/MadNLP/index.html @@ -43,4 +43,4 @@ author={Shin, Sungho and Coffrin, Carleton and Sundar, Kaarthik and Zavala, Victor M}, journal={arXiv preprint arXiv:2010.02404}, year={2020} -}

    Supporting MadNLP.jl

    +}

    Supporting MadNLP.jl

    diff --git a/previews/PR3913/packages/Manopt/index.html b/previews/PR3913/packages/Manopt/index.html index cbcd04cfa1a..980a66039bc 100644 --- a/previews/PR3913/packages/Manopt/index.html +++ b/previews/PR3913/packages/Manopt/index.html @@ -30,4 +30,4 @@ TITLE = {Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds}, VOLUME = {49}, YEAR = {2023} -}

    as well. Note that all citations are in BibLaTeX format.

    Manopt.jl belongs to the Manopt family:

    Did you use Manopt.jl somewhere? Let us know! We'd love to collect those here as well.

    +}

    as well. Note that all citations are in BibLaTeX format.

    Manopt.jl belongs to the Manopt family:

    Did you use Manopt.jl somewhere? Let us know! We'd love to collect those here as well.

    diff --git a/previews/PR3913/packages/MathOptAI/index.html b/previews/PR3913/packages/MathOptAI/index.html index 18e33684cc0..5a1cd7b3962 100644 --- a/previews/PR3913/packages/MathOptAI/index.html +++ b/previews/PR3913/packages/MathOptAI/index.html @@ -31,4 +31,4 @@ moai_SoftMax[7] moai_SoftMax[8] moai_SoftMax[9] - moai_SoftMax[10]

    Documentation

    Documentation is available at https://lanl-ansi.github.io/MathOptAI.jl.

    Getting help

    For help, questions, comments, and suggestions, please open a GitHub issue.

    Inspiration

    This project is mainly inspired by two existing projects:

    Other works, from which we took less inspiration, include:

    The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.

    López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632

    + moai_SoftMax[10]

    Documentation

    Documentation is available at https://lanl-ansi.github.io/MathOptAI.jl.

    Getting help

    For help, questions, comments, and suggestions, please open a GitHub issue.

    Inspiration

    This project is mainly inspired by two existing projects:

    Other works, from which we took less inspiration, include:

    The 2024 paper of López-Flores et al. is an excellent summary of the state of the field at the time that we started development of MathOptAI.

    López-Flores, F.J., Ramírez-Márquez, C., Ponce-Ortega J.M. (2024). Process Systems Engineering Tools for Optimization of Trained Machine Learning Models: Comparative and Perspective. Industrial & Engineering Chemistry Research, 63(32), 13966-13979. DOI: 10.1021/acs.iecr.4c00632

    diff --git a/previews/PR3913/packages/MathOptSymbolicAD/index.html b/previews/PR3913/packages/MathOptSymbolicAD/index.html index 27b9adbc989..ddc9e081bce 100644 --- a/previews/PR3913/packages/MathOptSymbolicAD/index.html +++ b/previews/PR3913/packages/MathOptSymbolicAD/index.html @@ -18,4 +18,4 @@ optimize!(model)

    Background

    MathOptSymbolicAD is inspired by Hassan Hijazi's work on coin-or/gravity, a high-performance algebraic modeling language in C++.

    Hassan made the following observations:

    • For large scale models, symbolic differentiation is slower than other automatic differentiation techniques.
    • However, most large-scale nonlinear programs have a lot of structure.
    • Gravity asks the user to provide structure in the form of template constraints, where the user gives the symbolic form of the constraint as well as a set of data to convert from a symbolic form to the numerical form.
    • Instead of differentiating each constraint in its numerical form, we can compute one symbolic derivative of the constraint in symbolic form, and then plug in the data in to get the numerical derivative of each function.
    • As a final step, if users don't provide the structure, we can still infer it –perhaps with less accuracy–by comparing the expression tree of each constraint.

    The symbolic differentiation approach of Gravity works well when the problem is large with few unique constraints. For example, a model like:

    model = Model()
 @variable(model, 0 <= x[1:10_000] <= 1)
 @constraint(model, [i=1:10_000], sin(x[i]) <= 1)
-@objective(model, Max, sum(x))

    is ideal, because although the Jacobian matrix has 10,000 rows, we can compute the derivative of sin(x[i]) as cos(x[i]), and then fill in the Jacobian by evaluating the derivative function instead of having to differentiation 10,000 expressions.

    The symbolic differentiation approach of Gravity works poorly if there are a large number of unique constraints in the model (which would require a lot of expressions to be symbolically differentiated), or if the nonlinear functions contain a large number of nonlinear terms (which would make the symbolic derivative expensive to compute).

    For more details, see Oscar's JuMP-dev 2022 talk, although note that the syntax has changed since the original recording.

    +@objective(model, Max, sum(x))

    is ideal, because although the Jacobian matrix has 10,000 rows, we can compute the derivative of sin(x[i]) as cos(x[i]), and then fill in the Jacobian by evaluating the derivative function instead of having to differentiation 10,000 expressions.

    The symbolic differentiation approach of Gravity works poorly if there are a large number of unique constraints in the model (which would require a lot of expressions to be symbolically differentiated), or if the nonlinear functions contain a large number of nonlinear terms (which would make the symbolic derivative expensive to compute).

    For more details, see Oscar's JuMP-dev 2022 talk, although note that the syntax has changed since the original recording.

    diff --git a/previews/PR3913/packages/MiniZinc/index.html b/previews/PR3913/packages/MiniZinc/index.html index 64efceac077..2582942b309 100644 --- a/previews/PR3913/packages/MiniZinc/index.html +++ b/previews/PR3913/packages/MiniZinc/index.html @@ -53,4 +53,4 @@ @constraint(model, x in MOI.AllDifferent(3)) @objective(model, Max, sum(i * x[i] for i in 1:3)) optimize!(model) -@show value.(x)

    MathOptInterface API

    The MiniZinc Optimizer{T} supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    Set options using MOI.RawOptimizerAttribute in MOI or set_attribute in JuMP.

    MiniZinc.jl supports the following options:

    • model_filename::String = "": the location at which to write out the .mzn file during optimization. This option can be helpful during debugging. If left empty, a temporary file will be used instead.

    • MOI.SolutionLimit: set this option to a positive integer to return up to the limit number of solutions.

    +@show value.(x)

    MathOptInterface API

    The MiniZinc Optimizer{T} supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Options

    Set options using MOI.RawOptimizerAttribute in MOI or set_attribute in JuMP.

    MiniZinc.jl supports the following options:

    • model_filename::String = "": the location at which to write out the .mzn file during optimization. This option can be helpful during debugging. If left empty, a temporary file will be used instead.

    • MOI.SolutionLimit: set this option to a positive integer to return up to the limit number of solutions.

    diff --git a/previews/PR3913/packages/MosekTools/index.html b/previews/PR3913/packages/MosekTools/index.html index 12291fc50c5..99b82966fa9 100644 --- a/previews/PR3913/packages/MosekTools/index.html +++ b/previews/PR3913/packages/MosekTools/index.html @@ -7,4 +7,4 @@ using MosekTools model = Model(Mosek.Optimizer) set_attribute(model, "QUIET", true) -set_attribute(model, "INTPNT_CO_TOL_DFEAS", 1e-7)

    Options

    The parameter QUIET is a special parameter that when set to true disables all Mosek printing output.

    All other parameters can be found in the Mosek documentation.

    Note that the prefix MSK_IPAR_ (for integer parameters), MSK_DPAR_ (for floating point parameters) or MSK_SPAR_ (for string parameters) are optional. If they are not given, they are inferred from the type of the value. For example, in the example above, as 1e-7 is a floating point number, the parameters name used is MSK_DPAR_INTPNT_CO_TOL_DFEAS.

    +set_attribute(model, "INTPNT_CO_TOL_DFEAS", 1e-7)

    Options

    The parameter QUIET is a special parameter that when set to true disables all Mosek printing output.

    All other parameters can be found in the Mosek documentation.

    Note that the prefix MSK_IPAR_ (for integer parameters), MSK_DPAR_ (for floating point parameters) or MSK_SPAR_ (for string parameters) are optional. If they are not given, they are inferred from the type of the value. For example, in the example above, as 1e-7 is a floating point number, the parameters name used is MSK_DPAR_INTPNT_CO_TOL_DFEAS.

    diff --git a/previews/PR3913/packages/MultiObjectiveAlgorithms/index.html b/previews/PR3913/packages/MultiObjectiveAlgorithms/index.html index 85618b3e444..fd795b53727 100644 --- a/previews/PR3913/packages/MultiObjectiveAlgorithms/index.html +++ b/previews/PR3913/packages/MultiObjectiveAlgorithms/index.html @@ -9,4 +9,4 @@ import MultiObjectiveAlgorithms as MOA model = JuMP.Model(() -> MOA.Optimizer(HiGHS.Optimizer)) set_attribute(model, MOA.Algorithm(), MOA.Dichotomy()) -set_attribute(model, MOA.SolutionLimit(), 4)

    Replace HiGHS.Optimizer with an optimizer capable of solving a single-objective instance of your optimization problem.

    You may set additional optimizer attributes, the supported attributes depend on the choice of solution algorithm.

    Algorithm

    Set the algorithm using the MOA.Algorithm() attribute.

    The value must be one of the algorithms supported by MOA:

    • MOA.Chalmet()
    • MOA.Dichotomy()
    • MOA.DominguezRios()
    • MOA.EpsilonConstraint()
    • MOA.Hierarchical()
    • MOA.KirlikSayin()
    • MOA.Lexicographic() [default]
    • MOA.TambyVanderpooten()

    Consult their docstrings for details.

    Other optimizer attributes

    There are a number of optimizer attributes supported by the algorithms in MOA.

    Each algorithm supports only a subset of the attributes. Consult the algorithm's docstring for details on which attributes it supports, and how it uses them in the solution process.

    • MOA.EpsilonConstraintStep()
    • MOA.LexicographicAllPermutations()
    • MOA.ObjectiveAbsoluteTolerance(index::Int)
    • MOA.ObjectivePriority(index::Int)
    • MOA.ObjectiveRelativeTolerance(index::Int)
    • MOA.ObjectiveWeight(index::Int)
    • MOA.SolutionLimit()
    • MOI.TimeLimitSec()
    +set_attribute(model, MOA.SolutionLimit(), 4)

    Replace HiGHS.Optimizer with an optimizer capable of solving a single-objective instance of your optimization problem.

    You may set additional optimizer attributes, the supported attributes depend on the choice of solution algorithm.

    Algorithm

    Set the algorithm using the MOA.Algorithm() attribute.

    The value must be one of the algorithms supported by MOA:

    • MOA.Chalmet()
    • MOA.Dichotomy()
    • MOA.DominguezRios()
    • MOA.EpsilonConstraint()
    • MOA.Hierarchical()
    • MOA.KirlikSayin()
    • MOA.Lexicographic() [default]
    • MOA.TambyVanderpooten()

    Consult their docstrings for details.

    Other optimizer attributes

    There are a number of optimizer attributes supported by the algorithms in MOA.

    Each algorithm supports only a subset of the attributes. Consult the algorithm's docstring for details on which attributes it supports, and how it uses them in the solution process.

    • MOA.EpsilonConstraintStep()
    • MOA.LexicographicAllPermutations()
    • MOA.ObjectiveAbsoluteTolerance(index::Int)
    • MOA.ObjectivePriority(index::Int)
    • MOA.ObjectiveRelativeTolerance(index::Int)
    • MOA.ObjectiveWeight(index::Int)
    • MOA.SolutionLimit()
    • MOI.TimeLimitSec()
    diff --git a/previews/PR3913/packages/NEOSServer/index.html b/previews/PR3913/packages/NEOSServer/index.html index b855886ffcf..1ac336ef687 100644 --- a/previews/PR3913/packages/NEOSServer/index.html +++ b/previews/PR3913/packages/NEOSServer/index.html @@ -27,4 +27,4 @@ results = neos_getFinalResults(server, job)

    Use with JuMP

    Use NEOSServer.jl with JuMP as follows:

    using JuMP, NEOSServer
 model = Model() do
     return NEOSServer.Optimizer(; email = "me@mydomain.com", solver = "Ipopt")
-end

    Note: NEOSServer.Optimizer is limited to the following solvers:

    • "CPLEX"
    • "FICO-Xpress"
    • "Ipopt"
    • "Knitro"
    • "MOSEK"
    • "OCTERACT"
    • "SNOPT"

    NEOS Limits

    NEOS currently limits jobs to an 8 hour time limit, 3 GB of memory, and a 16 MB submission file. If your model exceeds these limits, NEOSServer.jl may be unable to return useful information to the user.

    +end

    Note: NEOSServer.Optimizer is limited to the following solvers:

    • "CPLEX"
    • "FICO-Xpress"
    • "Ipopt"
    • "Knitro"
    • "MOSEK"
    • "OCTERACT"
    • "SNOPT"

    NEOS Limits

    NEOS currently limits jobs to an 8 hour time limit, 3 GB of memory, and a 16 MB submission file. If your model exceeds these limits, NEOSServer.jl may be unable to return useful information to the user.

    diff --git a/previews/PR3913/packages/NLopt/index.html b/previews/PR3913/packages/NLopt/index.html index 68ba198ddb9..6d046a83c5f 100644 --- a/previews/PR3913/packages/NLopt/index.html +++ b/previews/PR3913/packages/NLopt/index.html @@ -120,4 +120,4 @@ opt = Opt(:LD_MMA, 2) # Define problem solutions[i] = optimize(opt, rand(2)) -end

    Author

    This module was initially written by Steven G. Johnson, with subsequent contributions by several other authors (see the git history).

    +end

    Author

    This module was initially written by Steven G. Johnson, with subsequent contributions by several other authors (see the git history).

    diff --git a/previews/PR3913/packages/OSQP/index.html b/previews/PR3913/packages/OSQP/index.html index ff48533a428..87efb37d631 100644 --- a/previews/PR3913/packages/OSQP/index.html +++ b/previews/PR3913/packages/OSQP/index.html @@ -6,4 +6,4 @@
    GitHub

    OSQP.jl

    Build Status codecov.io

    OSQP.jl is a Julia wrapper for OSQP: the Operator Splitting QP Solver.

    License

    OSQP.jl is licensed under the Apache-2.0 license.

    The upstream solver, osqp/osqp is also licensed under the Apache-2.0 license.

    Installation

    Install OSQP.jl using the Julia package manager

    import Pkg
 Pkg.add("OSQP")

    Problem class

    The OSQP (Operator Splitting Quadratic Program) solver is a numerical optimization package for solving problems in the form

    minimize        0.5 x' P x + q' x
 
-subject to      l <= A x <= u

    where x in R^n is the optimization variable. The objective function is defined by a positive semidefinite matrix P in S^n_+ and vector q in R^n. The linear constraints are defined by matrix A in R^{m x n} and vectors l in R^m U {-inf}^m, u in R^m U {+inf}^m.

    Documentation

    Detailed documentation is available at https://osqp.org/.

    +subject to l <= A x <= u

    where x in R^n is the optimization variable. The objective function is defined by a positive semidefinite matrix P in S^n_+ and vector q in R^n. The linear constraints are defined by matrix A in R^{m x n} and vectors l in R^m U {-inf}^m, u in R^m U {+inf}^m.

    Documentation

    Detailed documentation is available at https://osqp.org/.

    diff --git a/previews/PR3913/packages/Optim/index.html b/previews/PR3913/packages/Optim/index.html index 86045dede5d..54b569e1de7 100644 --- a/previews/PR3913/packages/Optim/index.html +++ b/previews/PR3913/packages/Optim/index.html @@ -105,4 +105,4 @@ number = {24}, pages = {615}, doi = {10.21105/joss.00615} -} +} diff --git a/previews/PR3913/packages/PATHSolver/index.html b/previews/PR3913/packages/PATHSolver/index.html index 141bc783d3b..057c920240c 100644 --- a/previews/PR3913/packages/PATHSolver/index.html +++ b/previews/PR3913/packages/PATHSolver/index.html @@ -165,4 +165,4 @@ 0.8 1.2

    Thread safety

    PATH is not thread-safe and there are no known work-arounds. Do not run it in parallel using Threads.@threads. See issue #62 for more details.

    Factorization methods

    By default, PATHSolver.jl will download the LUSOL shared library. To use LUSOL, set the following options:

    model = Model(PATHSolver.Optimizer)
 set_optimizer_attribute(model, "factorization_method", "blu_lusol")
-set_optimizer_attribute(model, "factorization_library_name", PATHSolver.LUSOL_LIBRARY_PATH)

    To use factorization_method umfpack you will need the umfpack shared library that is available directly from the developers of that code for academic use.

    Manual installation

    By default PATHSolver.jl will download a copy of the libpath library. If you already have one installed and want to use that, set the PATH_JL_LOCATION environment variable to point to the libpath50.xx library.

    +set_optimizer_attribute(model, "factorization_library_name", PATHSolver.LUSOL_LIBRARY_PATH)

    To use factorization_method umfpack you will need the umfpack shared library that is available directly from the developers of that code for academic use.

    Manual installation

    By default PATHSolver.jl will download a copy of the libpath library. If you already have one installed and want to use that, set the PATH_JL_LOCATION environment variable to point to the libpath50.xx library.

    diff --git a/previews/PR3913/packages/Pajarito/index.html b/previews/PR3913/packages/Pajarito/index.html index 53f751b178e..338cb11a140 100644 --- a/previews/PR3913/packages/Pajarito/index.html +++ b/previews/PR3913/packages/Pajarito/index.html @@ -27,4 +27,4 @@ pages={249--293}, year={2020}, publisher={Springer} -}

    Note this paper describes a legacy MathProgBase version of Pajarito, which is available on the mathprogbase branch of this repository. Starting with version v0.8.0, Pajarito supports MathOptInterface instead of MathProgBase.

    +}

    Note this paper describes a legacy MathProgBase version of Pajarito, which is available on the mathprogbase branch of this repository. Starting with version v0.8.0, Pajarito supports MathOptInterface instead of MathProgBase.

    diff --git a/previews/PR3913/packages/ParametricOptInterface/index.html b/previews/PR3913/packages/ParametricOptInterface/index.html index da8b08d238f..a47b73ecd00 100644 --- a/previews/PR3913/packages/ParametricOptInterface/index.html +++ b/previews/PR3913/packages/ParametricOptInterface/index.html @@ -13,4 +13,4 @@ @objective(model, Min, 2x) optimize!(model) MOI.set(model, POI.ParameterValue(), p, 2.0) -optimize!(model)

    GSOC2020

    ParametricOptInterface began as a NumFOCUS sponsored Google Summer of Code (2020) project.

    +optimize!(model)

    GSOC2020

    ParametricOptInterface began as a NumFOCUS sponsored Google Summer of Code (2020) project.

    diff --git a/previews/PR3913/packages/Pavito/index.html b/previews/PR3913/packages/Pavito/index.html index 5ea144049f6..a3c591ff347 100644 --- a/previews/PR3913/packages/Pavito/index.html +++ b/previews/PR3913/packages/Pavito/index.html @@ -13,4 +13,4 @@ "cont_solver" => optimizer_with_attributes(Ipopt.Optimizer, "print_level" => 0), ), -)

    The algorithm implemented by Pavito itself is relatively simple; most of the hard work is performed by the MILP solver passed as mip_solver and the NLP solver passed as cont_solver.

    The performance of Pavito depends on these two types of solvers.

    For better performance, you should use a commercial MILP solver such as CPLEX or Gurobi.

    Options

    The following optimizer attributes can set to a Pavito.Optimizer to modify its behavior:

    • log_level::Int Verbosity flag: 0 for quiet, higher for basic solve info
    • timeout::Float64 Time limit for algorithm (in seconds)
    • rel_gap::Float64 Relative optimality gap termination condition
    • mip_solver_drives::Bool Let MILP solver manage convergence ("branch and cut")
    • mip_solver::MOI.OptimizerWithAttributes MILP solver
    • cont_solver::MOI.OptimizerWithAttributes Continuous NLP solver

    Pavito is not yet numerically robust and may require tuning of parameters to improve convergence.

    If the default parameters don't work for you, please let us know by opening an issue.

    For improved Pavito performance, MILP solver integrality tolerance and feasibility tolerances should typically be tightened, for example to 1e-8.

    Bug reports and support

    Please report any issues via the GitHub issue tracker. All types of issues are welcome and encouraged; this includes bug reports, documentation typos, feature requests, etc. The Optimization (Mathematical) category on Discourse is appropriate for general discussion.

    +)

    The algorithm implemented by Pavito itself is relatively simple; most of the hard work is performed by the MILP solver passed as mip_solver and the NLP solver passed as cont_solver.

    The performance of Pavito depends on these two types of solvers.

    For better performance, you should use a commercial MILP solver such as CPLEX or Gurobi.

    Options

    The following optimizer attributes can set to a Pavito.Optimizer to modify its behavior:

    • log_level::Int Verbosity flag: 0 for quiet, higher for basic solve info
    • timeout::Float64 Time limit for algorithm (in seconds)
    • rel_gap::Float64 Relative optimality gap termination condition
    • mip_solver_drives::Bool Let MILP solver manage convergence ("branch and cut")
    • mip_solver::MOI.OptimizerWithAttributes MILP solver
    • cont_solver::MOI.OptimizerWithAttributes Continuous NLP solver

    Pavito is not yet numerically robust and may require tuning of parameters to improve convergence.

    If the default parameters don't work for you, please let us know by opening an issue.

    For improved Pavito performance, MILP solver integrality tolerance and feasibility tolerances should typically be tightened, for example to 1e-8.

    Bug reports and support

    Please report any issues via the GitHub issue tracker. All types of issues are welcome and encouraged; this includes bug reports, documentation typos, feature requests, etc. The Optimization (Mathematical) category on Discourse is appropriate for general discussion.

    diff --git a/previews/PR3913/packages/Percival/index.html b/previews/PR3913/packages/Percival/index.html index 98ae8e7138e..6dc89bd4b05 100644 --- a/previews/PR3913/packages/Percival/index.html +++ b/previews/PR3913/packages/Percival/index.html @@ -22,4 +22,4 @@ [1.0], [1.0], ) -output = percival(nlp, verbose = 1)

    Bug reports and discussions

    If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.

    If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.

    +output = percival(nlp, verbose = 1)

    Bug reports and discussions

    If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.

    If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.

    diff --git a/previews/PR3913/packages/PiecewiseLinearOpt/index.html b/previews/PR3913/packages/PiecewiseLinearOpt/index.html index 1005cfd79eb..e3844d2abf1 100644 --- a/previews/PR3913/packages/PiecewiseLinearOpt/index.html +++ b/previews/PR3913/packages/PiecewiseLinearOpt/index.html @@ -41,4 +41,4 @@ (u, v) -> exp(u + v); method = :DisaggLogarithmic, ) -@objective(model, Min, z)

    Methods

    Supported univariate formulations:

    • Convex combination (:CC)
    • Multiple choice (:MC)
    • Native SOS2 branching (:SOS2)
    • Incremental (:Incremental)
    • Logarithmic (:Logarithmic; default)
    • Disaggregated Logarithmic (:DisaggLogarithmic)
    • Binary zig-zag (:ZigZag)
    • General integer zig-zag (:ZigZagInteger)

    Supported bivariate formulations for entire constraint:

    • Convex combination (:CC)
    • Multiple choice (:MC)
    • Disaggregated Logarithmic (:DisaggLogarithmic)

    Also, you can use any univariate formulation for bivariate functions as well. They will be used to impose two axis-aligned SOS2 constraints, along with the "6-stencil" formulation for the triangle selection portion of the constraint. See the associated paper for more details. In particular, the following are also acceptable bivariate formulation choices:

    • Native SOS2 branching (:SOS2)
    • Incremental (:Incremental)
    • Logarithmic (:Logarithmic)
    • Binary zig-zag (:ZigZag)
    • General integer zig-zag (:ZigZagInteger)
    +@objective(model, Min, z)

    Methods

    Supported univariate formulations:

    • Convex combination (:CC)
    • Multiple choice (:MC)
    • Native SOS2 branching (:SOS2)
    • Incremental (:Incremental)
    • Logarithmic (:Logarithmic; default)
    • Disaggregated Logarithmic (:DisaggLogarithmic)
    • Binary zig-zag (:ZigZag)
    • General integer zig-zag (:ZigZagInteger)

    Supported bivariate formulations for entire constraint:

    • Convex combination (:CC)
    • Multiple choice (:MC)
    • Disaggregated Logarithmic (:DisaggLogarithmic)

    Also, you can use any univariate formulation for bivariate functions as well. They will be used to impose two axis-aligned SOS2 constraints, along with the "6-stencil" formulation for the triangle selection portion of the constraint. See the associated paper for more details. In particular, the following are also acceptable bivariate formulation choices:

    • Native SOS2 branching (:SOS2)
    • Incremental (:Incremental)
    • Logarithmic (:Logarithmic)
    • Binary zig-zag (:ZigZag)
    • General integer zig-zag (:ZigZagInteger)
    diff --git a/previews/PR3913/packages/Plasmo/index.html b/previews/PR3913/packages/Plasmo/index.html index 840b0754a9a..466fca7d2d8 100644 --- a/previews/PR3913/packages/Plasmo/index.html +++ b/previews/PR3913/packages/Plasmo/index.html @@ -50,4 +50,4 @@ volume = {125}, year = {2019}, doi = {10.1016/j.compchemeng.2019.03.009} -}

    A pre-print of this paper can be found here

    +}

    A pre-print of this paper can be found here

    diff --git a/previews/PR3913/packages/PolyJuMP/index.html b/previews/PR3913/packages/PolyJuMP/index.html index 76ce40dd37f..80f46c57281 100644 --- a/previews/PR3913/packages/PolyJuMP/index.html +++ b/previews/PR3913/packages/PolyJuMP/index.html @@ -17,4 +17,4 @@ model = Model(optimizer_with_attributes( PolyJuMP.KKT.Optimizer, "solver" => HomotopyContinuation.SemialgebraicSetsHCSolver(), -))

    Documentation

    Documentation for PolyJuMP.jl is included in the documentation for SumOfSquares.jl.

    +))

    Documentation

    Documentation for PolyJuMP.jl is included in the documentation for SumOfSquares.jl.

    diff --git a/previews/PR3913/packages/ProxSDP/index.html b/previews/PR3913/packages/ProxSDP/index.html index 6e9fe69e11e..4f06312303c 100644 --- a/previews/PR3913/packages/ProxSDP/index.html +++ b/previews/PR3913/packages/ProxSDP/index.html @@ -56,4 +56,4 @@ publisher = {Taylor & Francis}, doi = {10.1080/02331934.2020.1823387}, URL = {https://doi.org/10.1080/02331934.2020.1823387} -}

    The preprint version of the paper can be found here.

    Disclaimer

    • ProxSDP is a research software, therefore it should not be used in production.
    • Please open an issue if you find any problems, developers will try to fix and find alternatives.
    • There is no continuous development for 32-bit systems, the package should work, but might reach some issues.
    • ProxSDP assumes primal and dual feasibility.

    ROAD MAP

    • Support for exponential and power cones
    • Warm start
    +}

    The preprint version of the paper can be found here.

    Disclaimer

    • ProxSDP is a research software, therefore it should not be used in production.
    • Please open an issue if you find any problems, developers will try to fix and find alternatives.
    • There is no continuous development for 32-bit systems, the package should work, but might reach some issues.
    • ProxSDP assumes primal and dual feasibility.

    ROAD MAP

    • Support for exponential and power cones
    • Warm start
    diff --git a/previews/PR3913/packages/SCIP/index.html b/previews/PR3913/packages/SCIP/index.html index ca91c251f5c..a8453e26b21 100644 --- a/previews/PR3913/packages/SCIP/index.html +++ b/previews/PR3913/packages/SCIP/index.html @@ -14,4 +14,4 @@ julia> Pkg.build("SCIP")

    Use with JuMP

    Use SCIP with JuMP as follows:

    using JuMP, SCIP
 model = Model(SCIP.Optimizer)
 set_attribute(model, "display/verblevel", 0)
-set_attribute(model, "limits/gap", 0.05)

    Options

    See the SCIP documentation for a list of supported options.

    MathOptInterface API

    The SCIP optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Design considerations

    Wrapping the public API

    All of the public API methods are wrapped and available within the SCIP package. This includes the scip_*.h and pub_*.h headers that are collected in scip.h, as well as all default constraint handlers (cons_*.h.)

    The wrapped functions do not transform any data structures and work on the raw pointers (for example, SCIP* in C, Ptr{SCIP_} in Julia). Convenience wrapper functions based on Julia types are added as needed.

    Memory management

    Programming with SCIP requires dealing with variable and constraint objects that use reference counting for memory management.

    The SCIP.Optimizer wrapper type collects lists of SCIP_VAR* and SCIP_CONS* under the hood, and it releases all references when it is garbage collected itself (via finalize).

    When adding a variable (add_variable) or a constraint (add_linear_constraint), an integer index is returned. This index can be used to retrieve the SCIP_VAR* or SCIP_CONS* pointer via get_var and get_cons respectively.

    Supported nonlinear operators

    Supported operators in nonlinear expressions are as follows:

    • +
    • -
    • *
    • /
    • ^
    • sqrt
    • exp
    • log
    • abs
    • cos
    • sin
    +set_attribute(model, "limits/gap", 0.05)

    Options

    See the SCIP documentation for a list of supported options.

    MathOptInterface API

    The SCIP optimizer supports the following constraints and attributes.

    List of supported objective functions:

    List of supported variable types:

    List of supported constraint types:

    List of supported model attributes:

    Design considerations

    Wrapping the public API

    All of the public API methods are wrapped and available within the SCIP package. This includes the scip_*.h and pub_*.h headers that are collected in scip.h, as well as all default constraint handlers (cons_*.h.)

    The wrapped functions do not transform any data structures and work on the raw pointers (for example, SCIP* in C, Ptr{SCIP_} in Julia). Convenience wrapper functions based on Julia types are added as needed.

    Memory management

    Programming with SCIP requires dealing with variable and constraint objects that use reference counting for memory management.

    The SCIP.Optimizer wrapper type collects lists of SCIP_VAR* and SCIP_CONS* under the hood, and it releases all references when it is garbage collected itself (via finalize).

    When adding a variable (add_variable) or a constraint (add_linear_constraint), an integer index is returned. This index can be used to retrieve the SCIP_VAR* or SCIP_CONS* pointer via get_var and get_cons respectively.

    Supported nonlinear operators

    Supported operators in nonlinear expressions are as follows:

    • +
    • -
    • *
    • /
    • ^
    • sqrt
    • exp
    • log
    • abs
    • cos
    • sin
    diff --git a/previews/PR3913/packages/SCS/index.html b/previews/PR3913/packages/SCS/index.html index f19b3d63332..944b38b6a45 100644 --- a/previews/PR3913/packages/SCS/index.html +++ b/previews/PR3913/packages/SCS/index.html @@ -53,4 +53,4 @@ julia> SCS.is_available(SCS.GpuIndirectSolver) true

    The GpuIndirectSolver is available on Linux x86_64 platform only.

    Low-level wrapper

    SCS.jl provides a low-level interface to solve a problem directly, without interfacing through MathOptInterface.

    This is an advanced interface with a risk of incorrect usage. For new users, we recommend that you use the JuMP or Convex interfaces instead.

    SCS solves a problem of the form:

    minimize        1/2 * x' * P * x + c' * x
 subject to      A * x + s = b
-                s in K

    where K is a product cone of:

    • zero cone
    • positive orthant { x | x ≥ 0 }
    • box cone { (t,x) | t*l ≤ x ≤ t*u}
    • second-order cone (SOC) { (t,x) | ||x||_2 ≤ t }
    • semi-definite cone (SDC) { X | X is psd }
    • exponential cone { (x,y,z) | y e^(x/y) ≤ z, y>0 }
    • power cone { (x,y,z) | x^a * y^(1-a) ≥ |z|, x ≥ 0, y ≥ 0 }
    • dual power cone { (u,v,w) | (u/a)^a * (v/(1-a))^(1-a) ≥ |w|, u ≥ 0, v ≥ 0 }.

    To solve this problem with SCS, call SCS.scs_solve; see the docstring for details.

    + s in K

    where K is a product cone of:

    • zero cone
    • positive orthant { x | x ≥ 0 }
    • box cone { (t,x) | t*l ≤ x ≤ t*u}
    • second-order cone (SOC) { (t,x) | ||x||_2 ≤ t }
    • semi-definite cone (SDC) { X | X is psd }
    • exponential cone { (x,y,z) | y e^(x/y) ≤ z, y>0 }
    • power cone { (x,y,z) | x^a * y^(1-a) ≥ |z|, x ≥ 0, y ≥ 0 }
    • dual power cone { (u,v,w) | (u/a)^a * (v/(1-a))^(1-a) ≥ |w|, u ≥ 0, v ≥ 0 }.

    To solve this problem with SCS, call SCS.scs_solve; see the docstring for details.

    diff --git a/previews/PR3913/packages/SDDP/index.html b/previews/PR3913/packages/SDDP/index.html index 4a3ec340a25..ebb3e62788d 100644 --- a/previews/PR3913/packages/SDDP/index.html +++ b/previews/PR3913/packages/SDDP/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub
    +
    GitHub
    diff --git a/previews/PR3913/packages/SDPA/index.html b/previews/PR3913/packages/SDPA/index.html index 925a1ece13c..c7d6bfd09a6 100644 --- a/previews/PR3913/packages/SDPA/index.html +++ b/previews/PR3913/packages/SDPA/index.html @@ -13,4 +13,4 @@ set_attribute(model, "Mode", SDPA.PARAMETER_STABLE_BUT_SLOW)

    Note that the parameters are set in the order they are given, so you can set a mode and then modify parameters from this mode.

    using JuMP, SDPA
 model = Model(SDPA.Optimizer)
 set_attribute(model, "Mode", SDPA.PARAMETER_STABLE_BUT_SLOW)
-set_attribute(model, "MaxIteration", 100)

    The choice of parameter mode has a large impact on the performance and stability of SDPA, and not necessarily in the way implied by the names of the modes; for example, PARAMETER_UNSTABLE_BUT_FAST can be more stable than the other modes for some problems. You should try each mode to see how it performs on your specific problem. See SDPA.jl#17 for more details.

    +set_attribute(model, "MaxIteration", 100)

    The choice of parameter mode has a large impact on the performance and stability of SDPA, and not necessarily in the way implied by the names of the modes; for example, PARAMETER_UNSTABLE_BUT_FAST can be more stable than the other modes for some problems. You should try each mode to see how it performs on your specific problem. See SDPA.jl#17 for more details.

    diff --git a/previews/PR3913/packages/SDPLR/index.html b/previews/PR3913/packages/SDPLR/index.html index c52b0cfcbe8..7923fda3703 100644 --- a/previews/PR3913/packages/SDPLR/index.html +++ b/previews/PR3913/packages/SDPLR/index.html @@ -50,4 +50,4 @@ sigma *= 2 end lambdaupdate = 0 -end +end diff --git a/previews/PR3913/packages/SDPNAL/index.html b/previews/PR3913/packages/SDPNAL/index.html index 14299683e17..a9d9124f3cc 100644 --- a/previews/PR3913/packages/SDPNAL/index.html +++ b/previews/PR3913/packages/SDPNAL/index.html @@ -18,4 +18,4 @@ '/path/to/SDPNALv1.0/solver:', ... '/path/to/SDPNALv1.0/solver_main_default:', ... '/path/to/SDPNALv1.0/util:', ... -% (...)

    If you have SDPT3 in addition to SDPNAL in the MATLAB path (that is, the toolbox/local/pathdef.m file) then you might have issues because both solvers define a validate function, and this might make SDPNAL call SDPT3's validate function instead of SDPT3's validate function.

    +% (...)

    If you have SDPT3 in addition to SDPNAL in the MATLAB path (that is, the toolbox/local/pathdef.m file) then you might have issues because both solvers define a validate function, and this might make SDPNAL call SDPT3's validate function instead of SDPT3's validate function.

    diff --git a/previews/PR3913/packages/SDPT3/index.html b/previews/PR3913/packages/SDPT3/index.html index fbe1392f850..91aeb5cb61b 100644 --- a/previews/PR3913/packages/SDPT3/index.html +++ b/previews/PR3913/packages/SDPT3/index.html @@ -29,4 +29,4 @@ julia> MATLAB.restoredefaultpath() -julia> MATLAB.mat"savepath" +julia> MATLAB.mat"savepath" diff --git a/previews/PR3913/packages/SeDuMi/index.html b/previews/PR3913/packages/SeDuMi/index.html index d5d44441183..21c87ab3b89 100644 --- a/previews/PR3913/packages/SeDuMi/index.html +++ b/previews/PR3913/packages/SeDuMi/index.html @@ -17,4 +17,4 @@ MATLAB.mat"install_sedumi" end -julia> MATLAB.mat"savepath" +julia> MATLAB.mat"savepath" diff --git a/previews/PR3913/packages/SumOfSquares/index.html b/previews/PR3913/packages/SumOfSquares/index.html index 0b6957e57d2..921fc854535 100644 --- a/previews/PR3913/packages/SumOfSquares/index.html +++ b/previews/PR3913/packages/SumOfSquares/index.html @@ -4,4 +4,4 @@ gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash});
    GitHub

    SumOfSquares.jl

    Build Status codecov

    SumOfSquares.jl is a JuMP extension that, when used in conjunction with MultivariatePolynomial and PolyJuMP, implements a sum of squares reformulation for polynomial optimization.

    License

    SumOfSquares.jl is licensed under the MIT license.

    Installation

    Install SumOfSquares using Pkg.add:

    import Pkg
-Pkg.add("SumOfSquares")

    Documentation

    See https://jump.dev/SumOfSquares.jl/stable for the most recently tagged version of the documentation.

    See https://jump.dev/SumOfSquares.jl/dev for the in-development version of the documentation.

    Presentations

    Some presentations on, or using, SumOfSquares (see blegat/SumOfSquaresSlides for the source code of the presentations):

    Citing

    See CITATION.bib.

    +Pkg.add("SumOfSquares")

    Documentation

    See https://jump.dev/SumOfSquares.jl/stable for the most recently tagged version of the documentation.

    See https://jump.dev/SumOfSquares.jl/dev for the in-development version of the documentation.

    Presentations

    Some presentations on, or using, SumOfSquares (see blegat/SumOfSquaresSlides for the source code of the presentations):

    Citing

    See CITATION.bib.

    diff --git a/previews/PR3913/packages/Tulip/index.html b/previews/PR3913/packages/Tulip/index.html index 502dab45046..7112fee3c08 100644 --- a/previews/PR3913/packages/Tulip/index.html +++ b/previews/PR3913/packages/Tulip/index.html @@ -28,4 +28,4 @@ language = {en}, url = {https://doi.org/10.1007/s12532-020-00200-8}, urldate = {2021-03-07}, -} +} diff --git a/previews/PR3913/packages/Xpress/index.html b/previews/PR3913/packages/Xpress/index.html index e7980cdd606..536a67f9afb 100644 --- a/previews/PR3913/packages/Xpress/index.html +++ b/previews/PR3913/packages/Xpress/index.html @@ -58,4 +58,4 @@ @test termination_status(model) == MOI.OPTIMAL @test primal_status(model) == MOI.FEASIBLE_POINT @test value(x) == 1 -@test value(y) == 2

    Environment variables

    • XPRESS_JL_SKIP_LIB_CHECK: Used to skip build lib check as previously described.
    • XPRESS_JL_NO_INFO: Disable license info log.
    • XPRESS_JL_NO_DEPS_ERROR: Disable error when do deps.jl file is found.
    • XPRESS_JL_NO_AUTO_INIT: Disable automatic run of Xpress.initialize(). Specially useful for explicitly loading the dynamic library.
    • XPRESS_JL_LIBRARY: Provide a custom path to libxprs
    • XPAUTH_PATH: Provide a custom path to the license file

    C API

    The C API can be accessed via Xpress.Lib.XPRSxx functions, where the names and arguments are identical to the C API.

    See the Xpress documentation for details.

    Documentation

    For more information, consult the FICO optimizer manual.

    +@test value(y) == 2

    Environment variables

    • XPRESS_JL_SKIP_LIB_CHECK: Used to skip build lib check as previously described.
    • XPRESS_JL_NO_INFO: Disable license info log.
    • XPRESS_JL_NO_DEPS_ERROR: Disable error when do deps.jl file is found.
    • XPRESS_JL_NO_AUTO_INIT: Disable automatic run of Xpress.initialize(). Specially useful for explicitly loading the dynamic library.
    • XPRESS_JL_LIBRARY: Provide a custom path to libxprs
    • XPAUTH_PATH: Provide a custom path to the license file

    C API

    The C API can be accessed via Xpress.Lib.XPRSxx functions, where the names and arguments are identical to the C API.

    See the Xpress documentation for details.

    Documentation

    For more information, consult the FICO optimizer manual.

    diff --git a/previews/PR3913/packages/solvers/index.html b/previews/PR3913/packages/solvers/index.html index 95a3ed3ff27..cbb1ec83cfd 100644 --- a/previews/PR3913/packages/solvers/index.html +++ b/previews/PR3913/packages/solvers/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Introduction

    This section of the documentation contains brief documentation for some of the solvers that JuMP supports. The list of solvers is not exhaustive, but instead is intended to help you discover commonly used solvers.

    Affiliation

    Packages beginning with jump-dev/ are developed and maintained by the JuMP developers. In many cases, these packages wrap external solvers that are not developed by the JuMP developers and, while the Julia packages are all open-source, in some cases the solvers themselves are closed source commercial products.

    Packages that do not begin with jump-dev/ are developed independently. The developers of these packages requested or consented to the inclusion of their README contents in the JuMP documentation for the benefit of users.

    Adding new solvers

    Written a solver? Add it to this section of the JuMP documentation by making a pull request to the docs/packages.toml file.

    +
    GitHub

    Introduction

    This section of the documentation contains brief documentation for some of the solvers that JuMP supports. The list of solvers is not exhaustive, but instead is intended to help you discover commonly used solvers.

    Affiliation

    Packages beginning with jump-dev/ are developed and maintained by the JuMP developers. In many cases, these packages wrap external solvers that are not developed by the JuMP developers and, while the Julia packages are all open-source, in some cases the solvers themselves are closed source commercial products.

    Packages that do not begin with jump-dev/ are developed independently. The developers of these packages requested or consented to the inclusion of their README contents in the JuMP documentation for the benefit of users.

    Adding new solvers

    Written a solver? Add it to this section of the JuMP documentation by making a pull request to the docs/packages.toml file.

    diff --git a/previews/PR3913/release_notes/index.html b/previews/PR3913/release_notes/index.html index 4e82e38a001..0c9289ee0a3 100644 --- a/previews/PR3913/release_notes/index.html +++ b/previews/PR3913/release_notes/index.html @@ -12,4 +12,4 @@ new_b = backend(model)
  • All usages of @SDconstraint are deprecated. The new syntax is @constraint(model, X >= Y, PSDCone()).
  • Creating a DenseAxisArray with a Number as an axis will now display a warning. This catches a common error in which users write @variable(model, x[length(S)]) instead of @variable(model, x[1:length(S)]).
  • The caching_mode argument to Model, for example, Model(caching_mode = MOIU.MANUAL) mode has been removed. For more control over the optimizer, use direct_model instead.
  • The previously deprecated lp_objective_perturbation_range and lp_rhs_perturbation_range functions have been removed. Use lp_sensitivity_report instead.
  • The .m fields of NonlinearExpression and NonlinearParameter have been renamed to .model.
  • Infinite variable bounds are now ignored. Thus, @variable(model, x <= Inf) will show has_upper_bound(x) == false. Previously, these bounds were passed through to the solvers which caused numerical issues for solvers expecting finite bounds.
  • The variable_type and constraint_type functions were removed. This should only affect users who previously wrote JuMP extensions. The functions can be deleted without consequence.
  • The internal functions moi_mode, moi_bridge_constraints, moi_add_constraint, and moi_add_to_function_constant are no longer exported.
  • The un-used method Containers.generate_container has been deleted.
  • The Containers API has been refactored, and _build_ref_sets is now public as Containers.build_ref_sets.
  • The parse_constraint_ methods for extending @constraint at parse time have been refactored in a breaking way. Consult the Extensions documentation for more details and examples.

    • Added

    • The TerminationStatusCode and ResultStatusCode enums are now exported by JuMP. Prefer termination_status(model) == OPTIMAL instead of == MOI.OPTIMAL, although the MOI. prefix way still works.
    • Copy a x::DenseAxisArray to an Array by calling Array(x).
    • NonlinearExpression is now a subtype of AbstractJuMPScalar
    • Constraints such as @constraint(model, x + 1 in MOI.Integer()) are now supported.
    • primal_feasibility_report now accepts a function as the first argument.
    • Scalar variables @variable(model, x[1:2] in MOI.Integer()) creates two variables, both of which are constrained to be in the set MOI.Integer.
    • Conic constraints can now be specified as inequalities under a different partial ordering. So @constraint(model, x - y in MOI.Nonnegatives()) can now be written as @constraint(model, x >= y, MOI.Nonnegatives()).
    • Names are now set for vectorized constraints.

    Fixed

    • Fixed a performance issue when show was called on a SparseAxisArray with a large number of elements.
    • Fixed a bug displaying barrier and simplex iterations in solution_summary.
    • Fixed a bug by implementing hash for DenseAxisArray and SparseAxisArray.
    • Names are now only set if the solver supports them. Previously, this prevented solvers such as Ipopt from being used with direct_model.
    • MutableArithmetics.Zero is converted into a 0.0 before being returned to the user. Previously, some calls to @expression would return the undocumented MutableArithmetics.Zero() object. One example is summing over an empty set @expression(model, sum(x[i] for i in 1:0)). You will now get 0.0 instead.
    • AffExpr and QuadExpr can now be used with == 0 instead of iszero. This fixes a number of issues relating to Julia standard libraries such as LinearAlgebra and SparseArrays.
    • Fixed a bug when registering a user-defined function with splatting.

    Other

    • The documentation is now available as a PDF.
    • The documentation now includes a full copy of the MathOptInterface documentation to make it easy to link concepts between the docs. (The MathOptInterface documentation has also been significantly improved.)
    • The documentation contains a large number of improvements and clarifications on a range of topics. Thanks to @sshin23, @DilumAluthge, and @jlwether.
    • The documentation is now built with Julia 1.6 instead of 1.0.
    • Various error messages have been improved to be more readable.

    Version 0.21.10 (September 4, 2021)

    Added

    • Added add_NL_expression
    • add_NL_xxx functions now support AffExpr and QuadExpr as terms

    Fixed

    • Fixed a bug in solution_summary
    • Fixed a bug in relax_integrality

    Other

    • Improved error message in lp_sensitivity_report

    Version 0.21.9 (August 1, 2021)

    Added

    • Containers now support arbitrary container types by passing the type to the container keyword and overloading Containers.container.
    • is_valid now supports nonlinear constraints
    • Added unsafe_backend for querying the inner-most optimizer of a JuMP model.
    • Nonlinear parameters now support the plural @NLparameters macro.
    • Containers (for example, DenseAxisArray) can now be used in vector-valued constraints.

    Other

    • Various improvements to the documentation.

    Version 0.21.8 (May 8, 2021)

    Added

    • The @constraint macro is now extendable in the same way as @variable.
    • AffExpr and QuadExpr can now be used in nonlinear macros.

    Fixed

    • Fixed a bug in lp_sensitivity_report.
    • Fixed an inference issue when creating empty SparseAxisArrays.

    Version 0.21.7 (April 12, 2021)

    Added

    • Added primal_feasibility_report, which can be used to check whether a primal point satisfies primal feasibility.
    • Added coefficient, which returns the coefficient associated with a variable in affine and quadratic expressions.
    • Added copy_conflict, which returns the IIS of an infeasible model.
    • Added solution_summary, which returns (and prints) a struct containing a summary of the solution.
    • Allow AbstractVector in vector constraints instead of just Vector.
    • Added latex_formulation(model) which returns an object representing the latex formulation of a model. Use print(latex_formulation(model)) to print the formulation as a string.
    • User-defined functions in nonlinear expressions are now automatically registered to aid quick model prototyping. However, a warning is printed to encourage the manual registration.
    • DenseAxisArray's now support broadcasting over multiple arrays.
    • Container indices can now be iterators of Base.SizeUnknown.

    Fixed

    • Fixed bug in rad2deg and deg2rad in nonlinear expressions.
    • Fixed a MethodError bug in Containers when forcing container type.
    • Allow partial slicing of a DenseAxisArray, resolving an issue from 2014.
    • Fixed a bug printing variable names in IJulia.
    • Ending an IJulia cell with model now prints a summary of the model (like in the REPL) not the latex formulation. Use print(model) to print the latex formulation.
    • Fixed a bug when copying models containing nested arrays.

    Other

    • Tutorials are now part of the documentation, and more refactoring has taken place.
    • Added JuliaFormatter added as a code formatter.
    • Added some precompilation statements to reduce initial latency.
    • Various improvements to error messages to make them more helpful.
    • Improved performance of value(::NonlinearExpression).
    • Improved performance of fix(::VariableRef).

    Version 0.21.6 (January 29, 2021)

    Added

    • Added support for skew symmetric variables via @variable(model, X[1:2, 1:2] in SkewSymmetricMatrixSpace()).
    • lp_sensitivity_report has been added which significantly improves the performance of querying the sensitivity summary of an LP. lp_objective_perturbation_range and lp_rhs_perturbation_range are deprecated.
    • Dual warm-starts are now supported with set_dual_start_value and dual_start_value.
    • ∈ (\in<tab>) can now be used in macros instead of = or in.
    • Use haskey(model::Model, key::Symbol) to check if a name key is registered in a model.
    • Added unregister(model::Model, key::Symbol) to unregister a name key from model.
    • Added callback_node_status for use in callbacks.
    • Added print_bridge_graph to visualize the bridging graph generated by MathOptInterface.
    • Improved error message for containers with duplicate indices.

    Fixed

    • Various fixes to pass tests on Julia 1.6.
    • Fixed a bug in the printing of nonlinear expressions in IJulia.
    • Fixed a bug when nonlinear expressions are passed to user-defined functions.
    • Some internal functions that were previously exported are now no longer exported.
    • Fixed a bug when relaxing a fixed binary variable.
    • Fixed a StackOverflowError that occurred when SparseAxisArrays had a large number of elements.
    • Removed an unnecessary type assertion in list_of_constraint_types.
    • Fixed a bug when copying models with registered expressions.

    Other

    • The documentation has been significantly overhauled. It now has distinct sections for the manual, API reference, and examples. The existing examples in /examples have now been moved to /docs/src/examples and rewritten using Literate.jl, and they are now included in the documentation.
    • JuliaFormatter has been applied to most of the codebase. This will continue to roll out over time, as we fix upstream issues in the formatter, and will eventually become compulsory.
    • The root cause of a large number of method invalidations has been resolved.
    • We switched continuous integration from Travis and Appveyor to GitHub Actions.

    Version 0.21.5 (September 18, 2020)

    Fixed

    • Fixed deprecation warnings
    • Throw DimensionMismatch for incompatibly sized functions and sets
    • Unify treatment of keys(x) on JuMP containers

    Version 0.21.4 (September 14, 2020)

    Added

    • Add debug info when adding unsupported constraints
    • Add relax_integrality for solving continuous relaxation
    • Allow querying constraint conflicts

    Fixed

    • Dispatch on Real for MOI.submit
    • Implement copy for CustomSet in tests
    • Don't export private macros
    • Fix invalid assertion in nonlinear
    • Error if constraint has NaN right-hand side
    • Improve speed of tests
    • Lots of work modularizing files in /test
    • Improve line numbers in macro error messages
    • Print nonlinear subexpressions
    • Various documentation updates
    • Dependency updates:
      • Datastructures 0.18
      • MathOptFormat v0.5
      • Prep for MathOptInterface 0.9.15

    Version 0.21.3 (June 18, 2020)

    • Added Special Order Sets (SOS1 and SOS2) to JuMP with default weights to ease the creation of such constraints (#2212).
    • Added functions simplex_iterations, barrier_iterations and node_count (#2201).
    • Added function reduced_cost (#2205).
    • Implemented callback_value for affine and quadratic expressions (#2231).
    • Support MutableArithmetics.Zero in objective and constraints (#2219).
    • Documentation improvements:
      • Mention tutorials in the docs (#2223).
      • Update COIN-OR links (#2242).
      • Explicit link to the documentation of MOI.FileFormats (#2253).
      • Typo fixes (#2261).
    • Containers improvements:
      • Fix Base.map for DenseAxisArray (#2235).
      • Throw BoundsError if number of indices is incorrect for DenseAxisArray and SparseAxisArray (#2240).
    • Extensibility improvements:
      • Implement a set_objective method fallback that redirects to set_objective_sense and set_objective_function (#2247).
      • Add parse_constraint method with arbitrary number of arguments (#2051).
      • Add parse_constraint_expr and parse_constraint_head (#2228).

    Version 0.21.2 (April 2, 2020)

    • Added relative_gap() to access MOI.RelativeGap() attribute (#2199).
    • Documentation fixes:
      • Added link to source for docstrings in the documentation (#2207).
      • Added docstring for @variables macro (#2216).
      • Typo fixes (#2177, #2184, #2182).
    • Implementation of methods for Base functions:
      • Implemented Base.empty! for JuMP.Model (#2198).
      • Implemented Base.conj for JuMP scalar types (#2209).

    Fixed

    • Fixed sum of expression with scalar product in macro (#2178).
    • Fixed writing of nonlinear models to MathOptFormat (#2181).
    • Fixed construction of empty SparseAxisArray (#2179).
    • Fixed constraint with zero function (#2188).

    Version 0.21.1 (Feb 18, 2020)

    • Improved the clarity of the with_optimizer deprecation warning.

    Version 0.21.0 (Feb 16, 2020)

    Breaking

    • Deprecated with_optimizer (#2090, #2084, #2141). You can replace with_optimizer by either nothing, optimizer_with_attributes or a closure:

      • replace with_optimizer(Ipopt.Optimizer) by Ipopt.Optimizer.
      • replace with_optimizer(Ipopt.Optimizer, max_cpu_time=60.0) by optimizer_with_attributes(Ipopt.Optimizer, "max_cpu_time" => 60.0).
      • replace with_optimizer(Gurobi.Optimizer, env) by () -> Gurobi.Optimizer(env).
      • replace with_optimizer(Gurobi.Optimizer, env, Presolve=0) by optimizer_with_attributes(() -> Gurobi.Optimizer(env), "Presolve" => 0).

      alternatively to optimizer_with_attributes, you can also set the attributes separately with set_optimizer_attribute.

    • Renamed set_parameter and set_parameters to set_optimizer_attribute and set_optimizer_attributes (#2150).

    • Broadcast should now be explicit inside macros. @SDconstraint(model, x >= 1) and @constraint(model, x + 1 in SecondOrderCone()) now throw an error instead of broadcasting 1 along the dimension of x (#2107).

    • @SDconstraint(model, x >= 0) is now equivalent to @constraint(model, x in PSDCone()) instead of @constraint(model, (x .- 0) in PSDCone()) (#2107).

    • The macros now create the containers with map instead of for loops, as a consequence, containers created by @expression can now have any element type and containers of constraint references now have concrete element types when possible. This fixes a long-standing issue where @expression could only be used to generate a collection of linear expressions. Now it works for quadratic expressions as well (#2070).

    • Calling deepcopy(::AbstractModel) now throws an error.

    • The constraint name is now printed in the model string (#2108).

    Added

    • Added support for solver-independent and solver-specific callbacks (#2101).
    • Added write_to_file and read_from_file, supported formats are CBF, LP, MathOptFormat, MPS and SDPA (#2114).
    • Added support for complementarity constraints (#2132).
    • Added support for indicator constraints (#2092).
    • Added support for querying multiple solutions with the result keyword (#2100).
    • Added support for constraining variables on creation (#2128).
    • Added method delete that deletes a vector of variables at once if it is supported by the underlying solver (#2135).
    • The arithmetic between JuMP expression has be refactored into the MutableArithmetics package (#2107).
    • Improved error on complex values in NLP (#1978).
    • Added an example of column generation (#2010).

    Fixed

    • Incorrect coefficients generated when using Symmetric variables (#2102)

    Version 0.20.1 (Oct 18, 2019)

    • Add sections on @variables and @constraints in the documentation (#2062).
    • Fixed product of sparse matrices for Julia v1.3 (#2063).
    • Added set_objective_coefficient to modify the coefficient of a linear term of the objective function (#2008).
    • Added set_time_limit_sec, unset_time_limit_sec and time_limit_sec to set and query the time limit for the solver in seconds (#2053).

    Version 0.20.0 (Aug 24, 2019)

    • Documentation updates.
    • Numerous bug fixes.
    • Better error messages (#1977, #1978, #1997, #2017).
    • Performance improvements (#1947, #2032).
    • Added LP sensitivity summary functions lp_objective_perturbation_range and lp_rhs_perturbation_range (#1917).
    • Added functions dual_objective_value, raw_status and set_parameter.
    • Added function set_objective_coefficient to modify the coefficient of a linear term of the objective (#2008).
    • Added functions set_normalized_rhs, normalized_rhs, and add_to_function_constant to modify and get the constant part of a constraint (#1935, #1960).
    • Added functions set_normalized_coefficient and normalized_coefficient to modify and get the coefficient of a linear term of a constraint (#1935, #1960).
    • Numerous other improvements in MOI 0.9, see the NEWS.md file of MOI for more details.

    Version 0.19.2 (June 8, 2019)

    • Fix a bug in derivatives that could arise in models with nested nonlinear subexpressions.

    Version 0.19.1 (May 12, 2019)

    • Usability and performance improvements.
    • Bug fixes.

    Version 0.19.0 (February 15, 2019)

    JuMP 0.19 contains significant breaking changes.

    Breaking

    • JuMP's abstraction layer for communicating with solvers changed from MathProgBase (MPB) to MathOptInterface (MOI). MOI addresses many longstanding design issues. (See @mlubin's slides from JuMP-dev 2018.) JuMP 0.19 is compatible only with solvers that have been updated for MOI. See the installation guide for a list of solvers that have and have not yet been updated.

    • Most solvers have been renamed to PackageName.Optimizer. For example, GurobiSolver() is now Gurobi.Optimizer.

    • Solvers are no longer added to a model via Model(solver = XXX(kwargs...)). Instead use Model(with_optimizer(XXX, kwargs...)). For example, Model(with_optimizer(Gurobi.Optimizer, OutputFlag=0)).

    • JuMP containers (for example, the objects returned by @variable) have been redesigned. Containers.SparseAxisArray replaces JuMPDict, JuMPArray was rewritten (inspired by AxisArrays) and renamed Containers.DenseAxisArray, and you can now request a container type with the container= keyword to the macros. See the corresponding documentation for more details.

    • The statuses returned by solvers have changed. See the possible status values here. The MOI statuses are much richer than the MPB statuses and can be used to distinguish between previously indistinguishable cases (for example, did the solver have a feasible solution when it stopped because of the time limit?).

    • Starting values are separate from result values. Use value to query the value of a variable in a solution. Use start_value and set_start_value to get and set an initial starting point provided to the solver. The solutions from previous solves are no longer automatically set as the starting points for the next solve.

    • The data structures for affine and quadratic expressions AffExpr and QuadExpr have changed. Internally, terms are stored in dictionaries instead of lists. Duplicate coefficients can no longer exist. Accessors and iteration methods have changed.

    • JuMPNLPEvaluator no longer includes the linear and quadratic parts of the model in the evaluation calls. These are now handled separately to allow NLP solvers that support various types of constraints.

    • JuMP solver-independent callbacks have been replaced by solver-specific callbacks. See your favorite solver for more details. (See the note below: No solver-specific callbacks are implemented yet.)

    • The norm() syntax is no longer recognized inside macros. Use the SecondOrderCone() set instead.

    • JuMP no longer performs automatic transformation between special quadratic forms and second-order cone constraints. Support for these constraint classes depends on the solver.

    • The symbols :Min and :Max are no longer used as optimization senses. Instead, JuMP uses the OptimizationSense enum from MathOptInterface. @objective(model, Max, ...), @objective(model, Min, ...), @NLobjective(model, Max, ...), and @objective(model, Min, ...) remain valid, but @objective(m, :Max, ...) is no longer accepted.

    • The sign conventions for duals has changed in some cases for consistency with conic duality (see the documentation). The shadow_price helper method returns duals with signs that match conventional LP interpretations of dual values as sensitivities of the objective value to relaxations of constraints.

    • @constraintref is no longer defined. Instead, create the appropriate container to hold constraint references manually. For example,

      constraints = Dict() # Optionally, specify types for improved performance.
 for i in 1:N
   constraints[i] = @constraint(model, ...)
-end

    • The lowerbound, upperbound, and basename keyword arguments to the @variable macro have been renamed to lower_bound, upper_bound, and base_name, for consistency with JuMP's new style recommendations.

    • We rely on broadcasting syntax to apply accessors to collections of variables, for example, value.(x) instead of getvalue(x) for collections. (Use value(x) when x is a scalar object.)

    Added

    • Splatting (like f(x...)) is recognized in restricted settings in nonlinear expressions.

    • Support for deleting constraints and variables.

    • The documentation has been completely rewritten using docstrings and Documenter.

    • Support for modeling mixed conic and quadratic models (for example, conic models with quadratic objectives and bi-linear matrix inequalities).

    • Significantly improved support for modeling new types of constraints and for extending JuMP's macros.

    • Support for providing dual warm starts.

    • Improved support for accessing solver-specific attributes (for example, the irreducible inconsistent subsystem).

    • Explicit control of whether symmetry-enforcing constraints are added to PSD constraints.

    • Support for modeling exponential cones.

    • Significant improvements in internal code quality and testing.

    • Style and naming guidelines.

    • Direct mode and manual mode provide explicit control over when copies of a model are stored or regenerated. See the corresponding documentation.

    Regressions

    There are known regressions from JuMP 0.18 that will be addressed in a future release (0.19.x or later):

    • Performance regressions in model generation (issue). Please file an issue anyway if you notice a significant performance regression. We have plans to address a number of performance issues, but we might not be aware of all of them.

    • Fast incremental NLP solves are not yet reimplemented (issue).

    • We do not yet have an implementation of solver-specific callbacks.

    • The column generation syntax in @variable has been removed (that is, the objective, coefficients, and inconstraints keyword arguments). Support for column generation will be re-introduced in a future release.

    • The ability to solve the continuous relaxation (that is, via solve(model; relaxation = true)) is not yet reimplemented (issue).

    Version 0.18.5 (December 1, 2018)

    • Support views in some derivative evaluation functions.
    • Improved compatibility with PackageCompiler.

    Version 0.18.4 (October 8, 2018)

    • Fix a bug in model printing on Julia 0.7 and 1.0.

    Version 0.18.3 (October 1, 2018)

    • Add support for Julia v1.0 (Thanks @ExpandingMan)
    • Fix matrix expressions with quadratic functions (#1508)

    Version 0.18.2 (June 10, 2018)

    • Fix a bug in second-order derivatives when expressions are present (#1319)
    • Fix a bug in @constraintref (#1330)

    Version 0.18.1 (April 9, 2018)

    • Fix for nested tuple destructuring (#1193)
    • Preserve internal model when relaxation=true (#1209)
    • Minor bug fixes and updates for example

    Version 0.18.0 (July 27, 2017)

    • Drop support for Julia 0.5.
    • Update for ForwardDiff 0.5.
    • Minor bug fixes.

    Version 0.17.1 (June 9, 2017)

    • Use of constructconstraint! in @SDconstraint.
    • Minor bug fixes.

    Version 0.17.0 (May 27, 2017)

    • Breaking change: Mixing quadratic and conic constraints is no longer supported.
    • Breaking change: The getvariable and getconstraint functions are replaced by indexing on the corresponding symbol. For instance, to access the variable with name x, one should now write m[:x] instead of getvariable(m, :x). As a consequence, creating a variable and constraint with the same name now triggers a warning, and accessing one of them afterwards throws an error. This change is breaking only in the latter case.
    • Addition of the getobjectivebound function that mirrors the functionality of the MathProgBase getobjbound function except that it takes into account transformations performed by JuMP.
    • Minor bug fixes.

    The following changes are primarily of interest to developers of JuMP extensions:

    • The new syntax @constraint(model, expr in Cone) creates the constraint ensuring that expr is inside Cone. The Cone argument is passed to constructconstraint! which enables the call to the dispatched to an extension.
    • The @variable macro now calls constructvariable! instead of directly calling the Variable constructor. Extra arguments and keyword arguments passed to @variable are passed to constructvariable! which enables the call to be dispatched to an extension.
    • Refactor the internal function conicdata (used build the MathProgBase conic model) into smaller sub-functions to make these parts reusable by extensions.

    Version 0.16.2 (March 28, 2017)

    • Minor bug fixes and printing tweaks
    • Address deprecation warnings for Julia 0.6

    Version 0.16.1 (March 7, 2017)

    • Better support for AbstractArray in JuMP (Thanks @tkoolen)
    • Minor bug fixes

    Version 0.16.0 (February 23, 2017)

    • Breaking change: JuMP no longer has a mechanism for selecting solvers by default (the previous mechanism was flawed and incompatible with Julia 0.6). Not specifying a solver before calling solve() will result in an error.
    • Breaking change: User-defined functions are no longer global. The first argument to JuMP.register is now a JuMP Model object within whose scope the function will be registered. Calling JuMP.register without a Model now produces an error.
    • Breaking change: Use the new JuMP.fix method to fix a variable to a value or to update the value to which a variable is fixed. Calling setvalue on a fixed variable now results in an error in order to avoid silent behavior changes. (Thanks @joaquimg)
    • Nonlinear expressions now print out similarly to linear/quadratic expressions (useful for debugging!)
    • New category keyword to @variable. Used for specifying categories of anonymous variables.
    • Compatibility with Julia 0.6-dev.
    • Minor fixes and improvements (Thanks @cossio, @ccoffrin, @blegat)

    Version 0.15.1 (January 31, 2017)

    • Bugfix for @LinearConstraints and friends

    Version 0.15.0 (December 22, 2016)

    • Julia 0.5.0 is the minimum required version for this release.
    • Document support for BARON solver
    • Enable info callbacks in more states than before, for example, for recording solutions. New when argument to addinfocallback (#814, thanks @yeesian)
    • Improved support for anonymous variables. This includes new warnings for potentially confusing use of the traditional non-anonymous syntax:
      • When multiple variables in a model are given the same name
      • When non-symbols are used as names, for example, @variable(m, x[1][1:N])
    • Improvements in iterating over JuMP containers (#836, thanks @IssamT)
    • Support for writing variable names in .lp file output (Thanks @leethargo)
    • Support for querying duals to SDP problems (Thanks @blegat)
    • The comprehension syntax with curly braces sum{}, prod{}, and norm2{} has been deprecated in favor of Julia's native comprehension syntax sum(), prod() and norm() as previously announced. (For early adopters of the new syntax, norm2() was renamed to norm() without deprecation.)
    • Unit tests rewritten to use Base.Test instead of FactCheck
    • Improved support for operations with matrices of JuMP types (Thanks @ExpandingMan)
    • The syntax to halt a solver from inside a callback has changed from throw(CallbackAbort()) to return JuMP.StopTheSolver
    • Minor bug fixes

    Version 0.14.2 (December 12, 2016)

    • Allow singleton anonymous variables (includes bugfix)

    Version 0.14.1 (September 12, 2016)

    • More consistent handling of states in informational callbacks, includes a new when parameter to addinfocallback for specifying in which state an informational callback should be called.

    Version 0.14.0 (August 7, 2016)

    • Compatibility with Julia 0.5 and ForwardDiff 0.2
    • Support for "anonymous" variables, constraints, expressions, and parameters, for example, x = @variable(m, [1:N]) instead of @variable(m, x[1:N])
    • Support for retrieving constraints from a model by name via getconstraint
    • @NLconstraint now returns constraint references (as expected).
    • Support for vectorized expressions within lazy constraints
    • On Julia 0.5, parse new comprehension syntax sum(x[i] for i in 1:N if isodd(i)) instead of sum{ x[i], i in 1:N; isodd(i) }. The old syntax with curly braces will be deprecated in JuMP 0.15.
    • Now possible to provide nonlinear expressions as "raw" Julia Expr objects instead of using JuMP's nonlinear macros. This input format is useful for programmatically generated expressions.
    • s/Mathematical Programming/Mathematical Optimization/
    • Support for local cuts (Thanks to @madanim, Mehdi Madani)
    • Document Xpress interface developed by @joaquimg, Joaquim Dias Garcia
    • Minor bug and deprecation fixes (Thanks @odow, @jrevels)

    Version 0.13.2 (May 16, 2016)

    • Compatibility update for MathProgBase

    Version 0.13.1 (May 3, 2016)

    • Fix broken deprecation for registerNLfunction.

    Version 0.13.0 (April 29, 2016)

    • Most exported methods and macros have been renamed to avoid camelCase. See the list of changes here. There is a 1-1 mapping from the old names to the new, and it is safe to simply replace the names to update existing models.
    • Specify variable lower/upper bounds in @variable using the lowerbound and upperbound keyword arguments.
    • Change name printed for variable using the basename keyword argument to @variable.
    • New @variables macro allows multi-line declaration of groups of variables.
    • A number of solver methods previously available only through MathProgBase are now exposed directly in JuMP. The fix was recorded live.
    • Compatibility fixes with Julia 0.5.
    • The "end" indexing syntax is no longer supported within JuMPArrays which do not use 1-based indexing until upstream issues are resolved, see here.

    Version 0.12.2 (March 9, 2016)

    • Small fixes for nonlinear optimization

    Version 0.12.1 (March 1, 2016)

    • Fix a regression in slicing for JuMPArrays (when not using 1-based indexing)

    Version 0.12.0 (February 27, 2016)

    • The automatic differentiation functionality has been completely rewritten with a number of user-facing changes:
      • @defExpr and @defNLExpr now take the model as the first argument. The previous one-argument version of @defExpr is deprecated; all expressions should be named. For example, replace @defExpr(2x+y) with @defExpr(jump_model, my_expr, 2x+y).
      • JuMP no longer uses Julia's variable binding rules for efficiently re-solving a sequence of nonlinear models. Instead, we have introduced nonlinear parameters. This is a breaking change, so we have added a warning message when we detect models that may depend on the old behavior.
      • Support for user-defined functions integrated within nonlinear JuMP expressions.
    • Replaced iteration over AffExpr with Number-like scalar iteration; previous iteration behavior is now available via linearterms(::AffExpr).
    • Stopping the solver via throw(CallbackAbort()) from a callback no longer triggers an exception. Instead, solve() returns UserLimit status.
    • getDual() now works for conic problems (Thanks @emreyamangil.)

    Version 0.11.3 (February 4, 2016)

    • Bug-fix for problems with quadratic objectives and semidefinite constraints

    Version 0.11.2 (January 14, 2016)

    • Compatibility update for Mosek

    Version 0.11.1 (December 1, 2015)

    • Remove usage of @compat in tests.
    • Fix updating quadratic objectives for nonlinear models.

    Version 0.11.0 (November 30, 2015)

    • Julia 0.4.0 is the minimum required version for this release.
    • Fix for scoping semantics of index variables in sum{}. Index variables no longer leak into the surrounding scope.
    • Addition of the solve(m::Model, relaxation=true) keyword argument to solve the standard continuous relaxation of model m
    • The getConstraintBounds() method allows access to the lower and upper bounds of all constraints in a (nonlinear) model.
    • Update for breaking changes in MathProgBase

    Version 0.10.3 (November 20, 2015)

    • Fix a rare error when parsing quadratic expressions
    • Fix Variable() constructor with default arguments
    • Detect unrecognized keywords in solve()

    Version 0.10.2 (September 28, 2015)

    • Fix for deprecation warnings

    Version 0.10.1 (September 3, 2015)

    • Fixes for ambiguity warnings.
    • Fix for breaking change in precompilation syntax in Julia 0.4-pre

    Version 0.10.0 (August 31, 2015)

    • Support (on Julia 0.4 and later) for conditions in indexing @defVar and @addConstraint constructs, for example, @defVar(m, x[i=1:5,j=1:5; i+j >= 3])
    • Support for vectorized operations on Variables and expressions. See the documentation for details.
    • New getVar() method to access variables in a model by name
    • Support for semidefinite programming.
    • Dual solutions are now available for general nonlinear problems. You may call getDual on a reference object for a nonlinear constraint, and getDual on a variable object for Lagrange multipliers from active bounds.
    • Introduce warnings for two common performance traps: too many calls to getValue() on a collection of variables and use of the + operator in a loop to sum expressions.
    • Second-order cone constraints can be written directly with the norm() and norm2{} syntax.
    • Implement MathProgBase interface for querying Hessian-vector products.
    • Iteration over JuMPContainers is deprecated; instead, use the keys and values functions, and zip(keys(d),values(d)) for the old behavior.
    • @defVar returns Array{Variable,N} when each of N index sets are of the form 1:nᵢ.
    • Module precompilation: on Julia 0.4 and later, using JuMP is now much faster.

    Version 0.9.3 (August 11, 2015)

    • Fixes for FactCheck testing on julia v0.4.

    Version 0.9.2 (June 27, 2015)

    • Fix bug in @addConstraints.

    Version 0.9.1 (April 25, 2015)

    • Fix for Julia 0.4-dev.
    • Small infrastructure improvements for extensions.

    Version 0.9.0 (April 18, 2015)

    • Comparison operators for constructing constraints (for example, 2x >= 1) have been deprecated. Instead, construct the constraints explicitly in the @addConstraint macro to add them to the model, or in the @LinearConstraint macro to create a stand-alone linear constraint instance.
    • getValue() method implemented to compute the value of a nonlinear subexpression
    • JuMP is now released under the Mozilla Public License version 2.0 (was previously LGPL). MPL is a copyleft license which is less restrictive than LGPL, especially for embedding JuMP within other applications.
    • A number of performance improvements in ReverseDiffSparse for computing derivatives.
    • MathProgBase.getsolvetime(m) now returns the solution time reported by the solver, if available. (Thanks @odow, Oscar Dowson)
    • Formatting fix for LP format output. (Thanks @sbebo, Leonardo Taccari).

    Version 0.8.0 (February 17, 2015)

    • Nonlinear subexpressions now supported with the @defNLExpr macro.
    • SCS supported for solving second-order conic problems.
    • setXXXCallback family deprecated in favor of addXXXCallback.
    • Multiple callbacks of the same type can be registered.
    • Added support for informational callbacks via addInfoCallback.
    • A CallbackAbort exception can be thrown from callback to safely exit optimization.

    Version 0.7.4 (February 4, 2015)

    • Reduced costs and linear constraint duals are now accessible when quadratic constraints are present.
    • Two-sided nonlinear constraints are supported.
    • Methods for accessing the number of variables and constraints in a model are renamed.
    • New default procedure for setting initial values in nonlinear optimization: project zero onto the variable bounds.
    • Small bug fixes.

    Version 0.7.3 (January 14, 2015)

    • Fix a method ambiguity conflict with Compose.jl (cosmetic fix)

    Version 0.7.2 (January 9, 2015)

    • Fix a bug in sum(::JuMPDict)
    • Added the setCategory function to change a variables category (for example, continuous or binary)

    after construction, and getCategory to retrieve the variable category.

    Version 0.7.1 (January 2, 2015)

    • Fix a bug in parsing linear expressions in macros. Affects only Julia 0.4 and later.

    Version 0.7.0 (December 29, 2014)

    Linear/quadratic/conic programming

    • Breaking change: The syntax for column-wise model generation has been changed to use keyword arguments in @defVar.
    • On Julia 0.4 and later, variables and coefficients may be multiplied in any order within macros. That is, variable*coefficient is now valid syntax.
    • ECOS supported for solving second-order conic problems.

    Nonlinear programming

    • Support for skipping model generation when solving a sequence of nonlinear models with changing data.
    • Fix a memory leak when solving a sequence of nonlinear models.
    • The @addNLConstraint macro now supports the three-argument version to define sets of nonlinear constraints.
    • KNITRO supported as a nonlinear solver.
    • Speed improvements for model generation.
    • The @addNLConstraints macro supports adding multiple (groups of) constraints at once. Syntax is similar to @addConstraints.
    • Discrete variables allowed in nonlinear problems for solvers which support them (currently only KNITRO).

    General

    • Starting values for variables may now be specified with @defVar(m, x, start=value).
    • The setSolver function allows users to change the solver subsequent to model creation.
    • Support for "fixed" variables via the @defVar(m, x == 1) syntax.
    • Unit tests rewritten to use FactCheck.jl, improved testing across solvers.

    Version 0.6.3 (October 19, 2014)

    • Fix a bug in multiplying two AffExpr objects.

    Version 0.6.2 (October 11, 2014)

    • Further improvements and bug fixes for printing.
    • Fixed a bug in @defExpr.
    • Support for accessing expression graphs through the MathProgBase NLP interface.

    Version 0.6.1 (September 19, 2014)

    • Improvements and bug fixes for printing.

    Version 0.6.0 (September 9, 2014)

    • Julia 0.3.0 is the minimum required version for this release.
    • buildInternalModel(m::Model) added to build solver-level model in memory without optimizing.
    • Deprecate load_model_only keyword argument to solve.
    • Add groups of constraints with @addConstraints macro.
    • Unicode operators now supported, including ∑ for sum, ∏ for prod, and ≤/≥
    • Quadratic constraints supported in @addConstraint macro.
    • Quadratic objectives supported in @setObjective macro.
    • MathProgBase solver-independent interface replaces Ipopt-specific interface for nonlinear problems
      • Breaking change: IpoptOptions no longer supported to specify solver options, use m = Model(solver=IpoptSolver(options...)) instead.
    • New solver interfaces: ECOS, NLopt, and nonlinear support for MOSEK
    • New option to control whether the lazy constraint callback is executed at each node in the B&B tree or just when feasible solutions are found
    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
    • Add support for index dependencies (for example, triangular indexing) in @defVar, @addConstraint, and @defExpr (for example, @defVar(m, x[i=1:10,j=i:10])).
      • This required some changes to the internal structure of JuMP containers, which may break code that explicitly stored JuMPDict objects.

    Version 0.5.8 (September 24, 2014)

    • Fix a bug with specifying solvers (affects Julia 0.2 only)

    Version 0.5.7 (September 5, 2014)

    • Fix a bug in printing models

    Version 0.5.6 (September 2, 2014)

    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
      • Breaking change: Syntax for Variable() constructor has changed (use of this interface remains discouraged)
    • Update for breaking changes in MathProgBase

    Version 0.5.5 (July 6, 2014)

    • Fix bug with problem modification: adding variables that did not appear in existing constraints or objective.

    Version 0.5.4 (June 19, 2014)

    • Update for breaking change in MathProgBase which reduces loading times for using JuMP
    • Fix error when MIPs not solved to optimality

    Version 0.5.3 (May 21, 2014)

    • Update for breaking change in ReverseDiffSparse

    Version 0.5.2 (May 9, 2014)

    • Fix compatibility with Julia 0.3 prerelease

    Version 0.5.1 (May 5, 2014)

    • Fix a bug in coefficient handling inside lazy constraints and user cuts

    Version 0.5.0 (May 2, 2014)

    • Support for nonlinear optimization with exact, sparse second-order derivatives automatically computed. Ipopt is currently the only solver supported.
    • getValue for AffExpr and QuadExpr
    • Breaking change: getSolverModel replaced by getInternalModel, which returns the internal MathProgBase-level model
    • Groups of constraints can be specified with @addConstraint (see documentation for details). This is not a breaking change.
    • dot(::JuMPDict{Variable},::JuMPDict{Variable}) now returns the corresponding quadratic expression.

    Version 0.4.1 (March 24, 2014)

    • Fix bug where change in objective sense was ignored when re-solving a model.
    • Fix issue with handling zero coefficients in AffExpr.

    Version 0.4.0 (March 10, 2014)

    • Support for SOS1 and SOS2 constraints.
    • Solver-independent callback for user heuristics.
    • dot and sum implemented for JuMPDict objects. Now you can say @addConstraint(m, dot(a,x) <= b).
    • Developers: support for extensions to JuMP. See definition of Model in src/JuMP.jl for more details.
    • Option to construct the low-level model before optimizing.

    Version 0.3.2 (February 17, 2014)

    • Improved model printing
      • Preliminary support for IJulia output

    Version 0.3.1 (January 30, 2014)

    • Documentation updates
    • Support for MOSEK
    • CPLEXLink renamed to CPLEX

    Version 0.3.0 (January 21, 2014)

    • Unbounded/infeasibility rays: getValue() will return the corresponding components of an unbounded ray when a model is unbounded, if supported by the selected solver. getDual() will return an infeasibility ray (Farkas proof) if a model is infeasible and the selected solver supports this feature.
    • Solver-independent callbacks for user generated cuts.
    • Use new interface for solver-independent QCQP.
    • setlazycallback renamed to setLazyCallback for consistency.

    Version 0.2.0 (December 15, 2013)

    Breaking

    • Objective sense is specified in setObjective instead of in the Model constructor.
    • lpsolver and mipsolver merged into single solver option.

    Added

    • Problem modification with efficient LP restarts and MIP warm-starts.
    • Relatedly, column-wise modeling now supported.
    • Solver-independent callbacks supported. Currently we support only a "lazy constraint" callback, which works with Gurobi, CPLEX, and GLPK. More callbacks coming soon.

    Version 0.1.2 (November 16, 2013)

    • Bug fixes for printing, improved error messages.
    • Allow AffExpr to be used in macros; for example, ex = y + z; @addConstraint(m, x + 2*ex <= 3)

    Version 0.1.1 (October 23, 2013)

    • Update for solver specification API changes in MathProgBase.

    Version 0.1.0 (October 3, 2013)

    • Initial public release.
    +end

  • The lowerbound, upperbound, and basename keyword arguments to the @variable macro have been renamed to lower_bound, upper_bound, and base_name, for consistency with JuMP's new style recommendations.

  • We rely on broadcasting syntax to apply accessors to collections of variables, for example, value.(x) instead of getvalue(x) for collections. (Use value(x) when x is a scalar object.)

    • Added

    • Splatting (like f(x...)) is recognized in restricted settings in nonlinear expressions.

    • Support for deleting constraints and variables.

    • The documentation has been completely rewritten using docstrings and Documenter.

    • Support for modeling mixed conic and quadratic models (for example, conic models with quadratic objectives and bi-linear matrix inequalities).

    • Significantly improved support for modeling new types of constraints and for extending JuMP's macros.

    • Support for providing dual warm starts.

    • Improved support for accessing solver-specific attributes (for example, the irreducible inconsistent subsystem).

    • Explicit control of whether symmetry-enforcing constraints are added to PSD constraints.

    • Support for modeling exponential cones.

    • Significant improvements in internal code quality and testing.

    • Style and naming guidelines.

    • Direct mode and manual mode provide explicit control over when copies of a model are stored or regenerated. See the corresponding documentation.

    Regressions

    There are known regressions from JuMP 0.18 that will be addressed in a future release (0.19.x or later):

    • Performance regressions in model generation (issue). Please file an issue anyway if you notice a significant performance regression. We have plans to address a number of performance issues, but we might not be aware of all of them.

    • Fast incremental NLP solves are not yet reimplemented (issue).

    • We do not yet have an implementation of solver-specific callbacks.

    • The column generation syntax in @variable has been removed (that is, the objective, coefficients, and inconstraints keyword arguments). Support for column generation will be re-introduced in a future release.

    • The ability to solve the continuous relaxation (that is, via solve(model; relaxation = true)) is not yet reimplemented (issue).

    Version 0.18.5 (December 1, 2018)

    • Support views in some derivative evaluation functions.
    • Improved compatibility with PackageCompiler.

    Version 0.18.4 (October 8, 2018)

    • Fix a bug in model printing on Julia 0.7 and 1.0.

    Version 0.18.3 (October 1, 2018)

    • Add support for Julia v1.0 (Thanks @ExpandingMan)
    • Fix matrix expressions with quadratic functions (#1508)

    Version 0.18.2 (June 10, 2018)

    • Fix a bug in second-order derivatives when expressions are present (#1319)
    • Fix a bug in @constraintref (#1330)

    Version 0.18.1 (April 9, 2018)

    • Fix for nested tuple destructuring (#1193)
    • Preserve internal model when relaxation=true (#1209)
    • Minor bug fixes and updates for example

    Version 0.18.0 (July 27, 2017)

    • Drop support for Julia 0.5.
    • Update for ForwardDiff 0.5.
    • Minor bug fixes.

    Version 0.17.1 (June 9, 2017)

    • Use of constructconstraint! in @SDconstraint.
    • Minor bug fixes.

    Version 0.17.0 (May 27, 2017)

    • Breaking change: Mixing quadratic and conic constraints is no longer supported.
    • Breaking change: The getvariable and getconstraint functions are replaced by indexing on the corresponding symbol. For instance, to access the variable with name x, one should now write m[:x] instead of getvariable(m, :x). As a consequence, creating a variable and constraint with the same name now triggers a warning, and accessing one of them afterwards throws an error. This change is breaking only in the latter case.
    • Addition of the getobjectivebound function that mirrors the functionality of the MathProgBase getobjbound function except that it takes into account transformations performed by JuMP.
    • Minor bug fixes.

    The following changes are primarily of interest to developers of JuMP extensions:

    • The new syntax @constraint(model, expr in Cone) creates the constraint ensuring that expr is inside Cone. The Cone argument is passed to constructconstraint! which enables the call to the dispatched to an extension.
    • The @variable macro now calls constructvariable! instead of directly calling the Variable constructor. Extra arguments and keyword arguments passed to @variable are passed to constructvariable! which enables the call to be dispatched to an extension.
    • Refactor the internal function conicdata (used build the MathProgBase conic model) into smaller sub-functions to make these parts reusable by extensions.

    Version 0.16.2 (March 28, 2017)

    • Minor bug fixes and printing tweaks
    • Address deprecation warnings for Julia 0.6

    Version 0.16.1 (March 7, 2017)

    • Better support for AbstractArray in JuMP (Thanks @tkoolen)
    • Minor bug fixes

    Version 0.16.0 (February 23, 2017)

    • Breaking change: JuMP no longer has a mechanism for selecting solvers by default (the previous mechanism was flawed and incompatible with Julia 0.6). Not specifying a solver before calling solve() will result in an error.
    • Breaking change: User-defined functions are no longer global. The first argument to JuMP.register is now a JuMP Model object within whose scope the function will be registered. Calling JuMP.register without a Model now produces an error.
    • Breaking change: Use the new JuMP.fix method to fix a variable to a value or to update the value to which a variable is fixed. Calling setvalue on a fixed variable now results in an error in order to avoid silent behavior changes. (Thanks @joaquimg)
    • Nonlinear expressions now print out similarly to linear/quadratic expressions (useful for debugging!)
    • New category keyword to @variable. Used for specifying categories of anonymous variables.
    • Compatibility with Julia 0.6-dev.
    • Minor fixes and improvements (Thanks @cossio, @ccoffrin, @blegat)

    Version 0.15.1 (January 31, 2017)

    • Bugfix for @LinearConstraints and friends

    Version 0.15.0 (December 22, 2016)

    • Julia 0.5.0 is the minimum required version for this release.
    • Document support for BARON solver
    • Enable info callbacks in more states than before, for example, for recording solutions. New when argument to addinfocallback (#814, thanks @yeesian)
    • Improved support for anonymous variables. This includes new warnings for potentially confusing use of the traditional non-anonymous syntax:
      • When multiple variables in a model are given the same name
      • When non-symbols are used as names, for example, @variable(m, x[1][1:N])
    • Improvements in iterating over JuMP containers (#836, thanks @IssamT)
    • Support for writing variable names in .lp file output (Thanks @leethargo)
    • Support for querying duals to SDP problems (Thanks @blegat)
    • The comprehension syntax with curly braces sum{}, prod{}, and norm2{} has been deprecated in favor of Julia's native comprehension syntax sum(), prod() and norm() as previously announced. (For early adopters of the new syntax, norm2() was renamed to norm() without deprecation.)
    • Unit tests rewritten to use Base.Test instead of FactCheck
    • Improved support for operations with matrices of JuMP types (Thanks @ExpandingMan)
    • The syntax to halt a solver from inside a callback has changed from throw(CallbackAbort()) to return JuMP.StopTheSolver
    • Minor bug fixes

    Version 0.14.2 (December 12, 2016)

    • Allow singleton anonymous variables (includes bugfix)

    Version 0.14.1 (September 12, 2016)

    • More consistent handling of states in informational callbacks, includes a new when parameter to addinfocallback for specifying in which state an informational callback should be called.

    Version 0.14.0 (August 7, 2016)

    • Compatibility with Julia 0.5 and ForwardDiff 0.2
    • Support for "anonymous" variables, constraints, expressions, and parameters, for example, x = @variable(m, [1:N]) instead of @variable(m, x[1:N])
    • Support for retrieving constraints from a model by name via getconstraint
    • @NLconstraint now returns constraint references (as expected).
    • Support for vectorized expressions within lazy constraints
    • On Julia 0.5, parse new comprehension syntax sum(x[i] for i in 1:N if isodd(i)) instead of sum{ x[i], i in 1:N; isodd(i) }. The old syntax with curly braces will be deprecated in JuMP 0.15.
    • Now possible to provide nonlinear expressions as "raw" Julia Expr objects instead of using JuMP's nonlinear macros. This input format is useful for programmatically generated expressions.
    • s/Mathematical Programming/Mathematical Optimization/
    • Support for local cuts (Thanks to @madanim, Mehdi Madani)
    • Document Xpress interface developed by @joaquimg, Joaquim Dias Garcia
    • Minor bug and deprecation fixes (Thanks @odow, @jrevels)

    Version 0.13.2 (May 16, 2016)

    • Compatibility update for MathProgBase

    Version 0.13.1 (May 3, 2016)

    • Fix broken deprecation for registerNLfunction.

    Version 0.13.0 (April 29, 2016)

    • Most exported methods and macros have been renamed to avoid camelCase. See the list of changes here. There is a 1-1 mapping from the old names to the new, and it is safe to simply replace the names to update existing models.
    • Specify variable lower/upper bounds in @variable using the lowerbound and upperbound keyword arguments.
    • Change name printed for variable using the basename keyword argument to @variable.
    • New @variables macro allows multi-line declaration of groups of variables.
    • A number of solver methods previously available only through MathProgBase are now exposed directly in JuMP. The fix was recorded live.
    • Compatibility fixes with Julia 0.5.
    • The "end" indexing syntax is no longer supported within JuMPArrays which do not use 1-based indexing until upstream issues are resolved, see here.

    Version 0.12.2 (March 9, 2016)

    • Small fixes for nonlinear optimization

    Version 0.12.1 (March 1, 2016)

    • Fix a regression in slicing for JuMPArrays (when not using 1-based indexing)

    Version 0.12.0 (February 27, 2016)

    • The automatic differentiation functionality has been completely rewritten with a number of user-facing changes:
      • @defExpr and @defNLExpr now take the model as the first argument. The previous one-argument version of @defExpr is deprecated; all expressions should be named. For example, replace @defExpr(2x+y) with @defExpr(jump_model, my_expr, 2x+y).
      • JuMP no longer uses Julia's variable binding rules for efficiently re-solving a sequence of nonlinear models. Instead, we have introduced nonlinear parameters. This is a breaking change, so we have added a warning message when we detect models that may depend on the old behavior.
      • Support for user-defined functions integrated within nonlinear JuMP expressions.
    • Replaced iteration over AffExpr with Number-like scalar iteration; previous iteration behavior is now available via linearterms(::AffExpr).
    • Stopping the solver via throw(CallbackAbort()) from a callback no longer triggers an exception. Instead, solve() returns UserLimit status.
    • getDual() now works for conic problems (Thanks @emreyamangil.)

    Version 0.11.3 (February 4, 2016)

    • Bug-fix for problems with quadratic objectives and semidefinite constraints

    Version 0.11.2 (January 14, 2016)

    • Compatibility update for Mosek

    Version 0.11.1 (December 1, 2015)

    • Remove usage of @compat in tests.
    • Fix updating quadratic objectives for nonlinear models.

    Version 0.11.0 (November 30, 2015)

    • Julia 0.4.0 is the minimum required version for this release.
    • Fix for scoping semantics of index variables in sum{}. Index variables no longer leak into the surrounding scope.
    • Addition of the solve(m::Model, relaxation=true) keyword argument to solve the standard continuous relaxation of model m
    • The getConstraintBounds() method allows access to the lower and upper bounds of all constraints in a (nonlinear) model.
    • Update for breaking changes in MathProgBase

    Version 0.10.3 (November 20, 2015)

    • Fix a rare error when parsing quadratic expressions
    • Fix Variable() constructor with default arguments
    • Detect unrecognized keywords in solve()

    Version 0.10.2 (September 28, 2015)

    • Fix for deprecation warnings

    Version 0.10.1 (September 3, 2015)

    • Fixes for ambiguity warnings.
    • Fix for breaking change in precompilation syntax in Julia 0.4-pre

    Version 0.10.0 (August 31, 2015)

    • Support (on Julia 0.4 and later) for conditions in indexing @defVar and @addConstraint constructs, for example, @defVar(m, x[i=1:5,j=1:5; i+j >= 3])
    • Support for vectorized operations on Variables and expressions. See the documentation for details.
    • New getVar() method to access variables in a model by name
    • Support for semidefinite programming.
    • Dual solutions are now available for general nonlinear problems. You may call getDual on a reference object for a nonlinear constraint, and getDual on a variable object for Lagrange multipliers from active bounds.
    • Introduce warnings for two common performance traps: too many calls to getValue() on a collection of variables and use of the + operator in a loop to sum expressions.
    • Second-order cone constraints can be written directly with the norm() and norm2{} syntax.
    • Implement MathProgBase interface for querying Hessian-vector products.
    • Iteration over JuMPContainers is deprecated; instead, use the keys and values functions, and zip(keys(d),values(d)) for the old behavior.
    • @defVar returns Array{Variable,N} when each of N index sets are of the form 1:nᵢ.
    • Module precompilation: on Julia 0.4 and later, using JuMP is now much faster.

    Version 0.9.3 (August 11, 2015)

    • Fixes for FactCheck testing on julia v0.4.

    Version 0.9.2 (June 27, 2015)

    • Fix bug in @addConstraints.

    Version 0.9.1 (April 25, 2015)

    • Fix for Julia 0.4-dev.
    • Small infrastructure improvements for extensions.

    Version 0.9.0 (April 18, 2015)

    • Comparison operators for constructing constraints (for example, 2x >= 1) have been deprecated. Instead, construct the constraints explicitly in the @addConstraint macro to add them to the model, or in the @LinearConstraint macro to create a stand-alone linear constraint instance.
    • getValue() method implemented to compute the value of a nonlinear subexpression
    • JuMP is now released under the Mozilla Public License version 2.0 (was previously LGPL). MPL is a copyleft license which is less restrictive than LGPL, especially for embedding JuMP within other applications.
    • A number of performance improvements in ReverseDiffSparse for computing derivatives.
    • MathProgBase.getsolvetime(m) now returns the solution time reported by the solver, if available. (Thanks @odow, Oscar Dowson)
    • Formatting fix for LP format output. (Thanks @sbebo, Leonardo Taccari).

    Version 0.8.0 (February 17, 2015)

    • Nonlinear subexpressions now supported with the @defNLExpr macro.
    • SCS supported for solving second-order conic problems.
    • setXXXCallback family deprecated in favor of addXXXCallback.
    • Multiple callbacks of the same type can be registered.
    • Added support for informational callbacks via addInfoCallback.
    • A CallbackAbort exception can be thrown from callback to safely exit optimization.

    Version 0.7.4 (February 4, 2015)

    • Reduced costs and linear constraint duals are now accessible when quadratic constraints are present.
    • Two-sided nonlinear constraints are supported.
    • Methods for accessing the number of variables and constraints in a model are renamed.
    • New default procedure for setting initial values in nonlinear optimization: project zero onto the variable bounds.
    • Small bug fixes.

    Version 0.7.3 (January 14, 2015)

    • Fix a method ambiguity conflict with Compose.jl (cosmetic fix)

    Version 0.7.2 (January 9, 2015)

    • Fix a bug in sum(::JuMPDict)
    • Added the setCategory function to change a variables category (for example, continuous or binary)

    after construction, and getCategory to retrieve the variable category.

    Version 0.7.1 (January 2, 2015)

    • Fix a bug in parsing linear expressions in macros. Affects only Julia 0.4 and later.

    Version 0.7.0 (December 29, 2014)

    Linear/quadratic/conic programming

    • Breaking change: The syntax for column-wise model generation has been changed to use keyword arguments in @defVar.
    • On Julia 0.4 and later, variables and coefficients may be multiplied in any order within macros. That is, variable*coefficient is now valid syntax.
    • ECOS supported for solving second-order conic problems.

    Nonlinear programming

    • Support for skipping model generation when solving a sequence of nonlinear models with changing data.
    • Fix a memory leak when solving a sequence of nonlinear models.
    • The @addNLConstraint macro now supports the three-argument version to define sets of nonlinear constraints.
    • KNITRO supported as a nonlinear solver.
    • Speed improvements for model generation.
    • The @addNLConstraints macro supports adding multiple (groups of) constraints at once. Syntax is similar to @addConstraints.
    • Discrete variables allowed in nonlinear problems for solvers which support them (currently only KNITRO).

    General

    • Starting values for variables may now be specified with @defVar(m, x, start=value).
    • The setSolver function allows users to change the solver subsequent to model creation.
    • Support for "fixed" variables via the @defVar(m, x == 1) syntax.
    • Unit tests rewritten to use FactCheck.jl, improved testing across solvers.

    Version 0.6.3 (October 19, 2014)

    • Fix a bug in multiplying two AffExpr objects.

    Version 0.6.2 (October 11, 2014)

    • Further improvements and bug fixes for printing.
    • Fixed a bug in @defExpr.
    • Support for accessing expression graphs through the MathProgBase NLP interface.

    Version 0.6.1 (September 19, 2014)

    • Improvements and bug fixes for printing.

    Version 0.6.0 (September 9, 2014)

    • Julia 0.3.0 is the minimum required version for this release.
    • buildInternalModel(m::Model) added to build solver-level model in memory without optimizing.
    • Deprecate load_model_only keyword argument to solve.
    • Add groups of constraints with @addConstraints macro.
    • Unicode operators now supported, including ∑ for sum, ∏ for prod, and ≤/≥
    • Quadratic constraints supported in @addConstraint macro.
    • Quadratic objectives supported in @setObjective macro.
    • MathProgBase solver-independent interface replaces Ipopt-specific interface for nonlinear problems
      • Breaking change: IpoptOptions no longer supported to specify solver options, use m = Model(solver=IpoptSolver(options...)) instead.
    • New solver interfaces: ECOS, NLopt, and nonlinear support for MOSEK
    • New option to control whether the lazy constraint callback is executed at each node in the B&B tree or just when feasible solutions are found
    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
    • Add support for index dependencies (for example, triangular indexing) in @defVar, @addConstraint, and @defExpr (for example, @defVar(m, x[i=1:10,j=i:10])).
      • This required some changes to the internal structure of JuMP containers, which may break code that explicitly stored JuMPDict objects.

    Version 0.5.8 (September 24, 2014)

    • Fix a bug with specifying solvers (affects Julia 0.2 only)

    Version 0.5.7 (September 5, 2014)

    • Fix a bug in printing models

    Version 0.5.6 (September 2, 2014)

    • Add support for semicontinuous and semi-integer variables for those solvers that support them.
      • Breaking change: Syntax for Variable() constructor has changed (use of this interface remains discouraged)
    • Update for breaking changes in MathProgBase

    Version 0.5.5 (July 6, 2014)

    • Fix bug with problem modification: adding variables that did not appear in existing constraints or objective.

    Version 0.5.4 (June 19, 2014)

    • Update for breaking change in MathProgBase which reduces loading times for using JuMP
    • Fix error when MIPs not solved to optimality

    Version 0.5.3 (May 21, 2014)

    • Update for breaking change in ReverseDiffSparse

    Version 0.5.2 (May 9, 2014)

    • Fix compatibility with Julia 0.3 prerelease

    Version 0.5.1 (May 5, 2014)

    • Fix a bug in coefficient handling inside lazy constraints and user cuts

    Version 0.5.0 (May 2, 2014)

    • Support for nonlinear optimization with exact, sparse second-order derivatives automatically computed. Ipopt is currently the only solver supported.
    • getValue for AffExpr and QuadExpr
    • Breaking change: getSolverModel replaced by getInternalModel, which returns the internal MathProgBase-level model
    • Groups of constraints can be specified with @addConstraint (see documentation for details). This is not a breaking change.
    • dot(::JuMPDict{Variable},::JuMPDict{Variable}) now returns the corresponding quadratic expression.

    Version 0.4.1 (March 24, 2014)

    • Fix bug where change in objective sense was ignored when re-solving a model.
    • Fix issue with handling zero coefficients in AffExpr.

    Version 0.4.0 (March 10, 2014)

    • Support for SOS1 and SOS2 constraints.
    • Solver-independent callback for user heuristics.
    • dot and sum implemented for JuMPDict objects. Now you can say @addConstraint(m, dot(a,x) <= b).
    • Developers: support for extensions to JuMP. See definition of Model in src/JuMP.jl for more details.
    • Option to construct the low-level model before optimizing.

    Version 0.3.2 (February 17, 2014)

    • Improved model printing
      • Preliminary support for IJulia output

    Version 0.3.1 (January 30, 2014)

    • Documentation updates
    • Support for MOSEK
    • CPLEXLink renamed to CPLEX

    Version 0.3.0 (January 21, 2014)

    • Unbounded/infeasibility rays: getValue() will return the corresponding components of an unbounded ray when a model is unbounded, if supported by the selected solver. getDual() will return an infeasibility ray (Farkas proof) if a model is infeasible and the selected solver supports this feature.
    • Solver-independent callbacks for user generated cuts.
    • Use new interface for solver-independent QCQP.
    • setlazycallback renamed to setLazyCallback for consistency.

    Version 0.2.0 (December 15, 2013)

    Breaking

    • Objective sense is specified in setObjective instead of in the Model constructor.
    • lpsolver and mipsolver merged into single solver option.

    Added

    • Problem modification with efficient LP restarts and MIP warm-starts.
    • Relatedly, column-wise modeling now supported.
    • Solver-independent callbacks supported. Currently we support only a "lazy constraint" callback, which works with Gurobi, CPLEX, and GLPK. More callbacks coming soon.

    Version 0.1.2 (November 16, 2013)

    • Bug fixes for printing, improved error messages.
    • Allow AffExpr to be used in macros; for example, ex = y + z; @addConstraint(m, x + 2*ex <= 3)

    Version 0.1.1 (October 23, 2013)

    • Update for solver specification API changes in MathProgBase.

    Version 0.1.0 (October 3, 2013)

    • Initial public release.
    diff --git a/previews/PR3913/should_i_use/index.html b/previews/PR3913/should_i_use/index.html index 026c47afccc..0217281cb05 100644 --- a/previews/PR3913/should_i_use/index.html +++ b/previews/PR3913/should_i_use/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Should you use JuMP?

    JuMP is an algebraic modeling language for mathematical optimization written in the Julia language.

    This page explains when you should consider using JuMP, and importantly, when you should not use JuMP.

    When should you use JuMP?

    You should use JuMP if you have a constrained optimization problem that is formulated using the language of mathematical programming, that is, the problem has:

    • a set of real- or complex-valued decision variables
    • a scalar- or vector-valued real objective function
    • a set of constraints.

    Key reasons to use JuMP include:

    • User friendliness
    • Solver independence
      • JuMP uses a generic solver-independent interface provided by the MathOptInterface package, making it easy to change between a number of open-source and commercial optimization software packages ("solvers"). The Supported solvers section contains a table of the currently supported solvers.
    • Ease of embedding
      • JuMP itself is written purely in Julia. Solvers are the only binary dependencies.
      • JuMP provides automatic installation of most solvers.
      • Because it is embedded in a general-purpose programming language, JuMP makes it easy to solve optimization problems as part of a larger workflow, for example, inside a simulation, behind a web server, or as a subproblem in a decomposition algorithm. As a trade-off, JuMP's syntax is constrained by the syntax and functionality available in Julia.
      • JuMP is MPL licensed, meaning that it can be embedded in commercial software that complies with the terms of the license.
    • Speed
      • Benchmarking has shown that JuMP can create problems at similar speeds to special-purpose modeling languages such as AMPL.
      • JuMP communicates with most solvers in memory, avoiding the need to write intermediary files.
    • Access to advanced algorithmic techniques
      • JuMP supports efficient in-memory re-solves of models.
      • JuMP provides access to solver-independent and solver-dependent Callbacks.

    When should you not use JuMP?

    JuMP supports a broad range of optimization classes. However, there are still some that it doesn't support, or that are better supported by other software packages.

    You want to optimize a complicated Julia function

    Packages in Julia compose well. It's common for people to pick two unrelated packages and use them in conjunction to create novel behavior. JuMP isn't one of those packages.

    If you want to optimize an ordinary differential equation from DifferentialEquations.jl or tune a neural network from Flux.jl, consider using other packages such as:

    Black-box, derivative free, or unconstrained optimization

    JuMP supports nonlinear programs with constraints and objectives containing user-defined operators. However, the functions must be automatically differentiable, or you need to provide explicit derivatives. (See User-defined operators for more information.)

    If your function is a black-box that is non-differentiable (for example, the function calls a simulation written in C++), JuMP is not the right tool for the job. This also applies if you want to use a derivative free method.

    Even if your problem is differentiable, if it is unconstrained there is limited benefit (and downsides in the form of more overhead) to using JuMP over tools which are concerned only with function minimization.

    Alternatives to consider are:

    Disciplined convex programming

    JuMP does not support disciplined convex programming (DCP).

    Alternatives to consider are:

    Note

    Convex.jl is also built on MathOptInterface, and shares the same set of underlying solvers. However, you input problems differently, and Convex.jl checks that the problem is DCP.

    Stochastic programming

    JuMP requires deterministic input data.

    If you have stochastic input data, consider using a JuMP extension such as:

    Polyhedral computations

    JuMP does not provide tools for working with the polyhedron formed by the set of linear constraints.

    Alternatives to consider are:

    +
    GitHub

    Should you use JuMP?

    JuMP is an algebraic modeling language for mathematical optimization written in the Julia language.

    This page explains when you should consider using JuMP, and importantly, when you should not use JuMP.

    When should you use JuMP?

    You should use JuMP if you have a constrained optimization problem that is formulated using the language of mathematical programming, that is, the problem has:

    • a set of real- or complex-valued decision variables
    • a scalar- or vector-valued real objective function
    • a set of constraints.

    Key reasons to use JuMP include:

    • User friendliness
    • Solver independence
      • JuMP uses a generic solver-independent interface provided by the MathOptInterface package, making it easy to change between a number of open-source and commercial optimization software packages ("solvers"). The Supported solvers section contains a table of the currently supported solvers.
    • Ease of embedding
      • JuMP itself is written purely in Julia. Solvers are the only binary dependencies.
      • JuMP provides automatic installation of most solvers.
      • Because it is embedded in a general-purpose programming language, JuMP makes it easy to solve optimization problems as part of a larger workflow, for example, inside a simulation, behind a web server, or as a subproblem in a decomposition algorithm. As a trade-off, JuMP's syntax is constrained by the syntax and functionality available in Julia.
      • JuMP is MPL licensed, meaning that it can be embedded in commercial software that complies with the terms of the license.
    • Speed
      • Benchmarking has shown that JuMP can create problems at similar speeds to special-purpose modeling languages such as AMPL.
      • JuMP communicates with most solvers in memory, avoiding the need to write intermediary files.
    • Access to advanced algorithmic techniques
      • JuMP supports efficient in-memory re-solves of models.
      • JuMP provides access to solver-independent and solver-dependent Callbacks.

    When should you not use JuMP?

    JuMP supports a broad range of optimization classes. However, there are still some that it doesn't support, or that are better supported by other software packages.

    You want to optimize a complicated Julia function

    Packages in Julia compose well. It's common for people to pick two unrelated packages and use them in conjunction to create novel behavior. JuMP isn't one of those packages.

    If you want to optimize an ordinary differential equation from DifferentialEquations.jl or tune a neural network from Flux.jl, consider using other packages such as:

    Black-box, derivative free, or unconstrained optimization

    JuMP supports nonlinear programs with constraints and objectives containing user-defined operators. However, the functions must be automatically differentiable, or you need to provide explicit derivatives. (See User-defined operators for more information.)

    If your function is a black-box that is non-differentiable (for example, the function calls a simulation written in C++), JuMP is not the right tool for the job. This also applies if you want to use a derivative free method.

    Even if your problem is differentiable, if it is unconstrained there is limited benefit (and downsides in the form of more overhead) to using JuMP over tools which are concerned only with function minimization.

    Alternatives to consider are:

    Disciplined convex programming

    JuMP does not support disciplined convex programming (DCP).

    Alternatives to consider are:

    Note

    Convex.jl is also built on MathOptInterface, and shares the same set of underlying solvers. However, you input problems differently, and Convex.jl checks that the problem is DCP.

    Stochastic programming

    JuMP requires deterministic input data.

    If you have stochastic input data, consider using a JuMP extension such as:

    Polyhedral computations

    JuMP does not provide tools for working with the polyhedron formed by the set of linear constraints.

    Alternatives to consider are:

    diff --git a/previews/PR3913/tutorials/algorithms/benders_decomposition/index.html b/previews/PR3913/tutorials/algorithms/benders_decomposition/index.html index ba990c2aa0e..ddaf4a33a3e 100644 --- a/previews/PR3913/tutorials/algorithms/benders_decomposition/index.html +++ b/previews/PR3913/tutorials/algorithms/benders_decomposition/index.html @@ -66,7 +66,7 @@ Dual objective value : NaN * Work counters - Solve time (sec) : 1.55663e-03 + Solve time (sec) : 1.90449e-03 Simplex iterations : 15 Barrier iterations : -1 Node count : 1 @@ -417,4 +417,4 @@ (3, 6) => 1.0 (4, 6) => 1.0 (5, 8) => 4.0 - (6, 8) => 2.0

    which is the same as the monolithic solution (because sum(y) >= 1 in the monolithic solution):

    feasible_inplace_solution == monolithic_solution
    true
    + (6, 8) => 2.0

    which is the same as the monolithic solution (because sum(y) >= 1 in the monolithic solution):

    feasible_inplace_solution == monolithic_solution
    true
    diff --git a/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/044e7623.svg b/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/09820ee9.svg similarity index 69% rename from previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/044e7623.svg rename to previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/09820ee9.svg index 865a977fc8f..a2bf8b2891a 100644 --- a/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/044e7623.svg +++ b/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/09820ee9.svg @@ -1,516 +1,516 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/37cf2941.svg b/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/509b86df.svg similarity index 72% rename from previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/37cf2941.svg rename to previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/509b86df.svg index acef2b0eb6e..93051511c7f 100644 --- a/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/37cf2941.svg +++ b/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/509b86df.svg @@ -1,350 +1,350 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/index.html b/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/index.html index 68d241475b4..337adb7122c 100644 --- a/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/index.html +++ b/previews/PR3913/tutorials/algorithms/cutting_stock_column_generation/index.html @@ -118,8 +118,8 @@ Dual objective value : NaN * Work counters - Solve time (sec) : 5.04970e+00 - Simplex iterations : 20396 + Solve time (sec) : 5.05041e+00 + Simplex iterations : 20589 Barrier iterations : -1 Node count : 0

    However, there is a formulation that solves much faster, and that is to use a column generation scheme.

    Column generation theory

    The key insight for column generation is to recognize that feasible columns in the $x$ matrix of variables encode cutting patterns.

    For example, if we look only at the roll $j=1$, then a feasible solution is:

    • $x_{1,1} = 1$ (1 unit of piece #1)
    • $x_{13,1} = 1$ (1 unit of piece #13)
    • All other $x_{i,1} = 0$

    Another solution is

    • $x_{20,1} = 19$ (19 unit of piece #20)
    • All other $x_{i,1} = 0$

    Cutting patterns like $x_{1,1} = 1$ and $x_{2,1} = 1$ are infeasible because the combined length is greater than $W$.

    Since there are a finite number of ways that we could cut a roll into a valid cutting pattern, we could create a set of all possible cutting patterns $p = 1,\ldots,P$, with data $a_{i,p}$ indicating how many units of piece $i$ we cut in pattern $p$. Then, we can formulate our mixed-integer linear program as:

    \[\begin{align} @@ -189,7 +189,7 @@ return plot end -plot_patterns(data, patterns)Example block output

    The base problem

    Using the initial set of patterns, we can create and optimize our base model:

    model = Model(HiGHS.Optimizer)
+plot_patterns(data, patterns)
    Example block output

    The base problem

    Using the initial set of patterns, we can create and optimize our base model:

    model = Model(HiGHS.Optimizer)
 set_silent(model)
 @variable(model, x[1:length(patterns)] >= 0, Int)
 @objective(model, Min, sum(x))
@@ -213,7 +213,7 @@
   Dual objective value : NaN
 
 * Work counters
-  Solve time (sec)   : 2.08855e-04
+  Solve time (sec)   : 1.45674e-04
   Simplex iterations : 0
   Barrier iterations : -1
   Node count         : 0
@@ -285,7 +285,7 @@
 [ Info: No new patterns, terminating the algorithm.

    We found lots of new patterns. Here's pattern 21:

    patterns[21]
    20-element SparseArrays.SparseVector{Int64, Int64} with 3 stored entries:
   [9 ]  =  1
   [13]  =  2
-  [17]  =  1

    Let's have a look at the patterns now:

    plot_patterns(data, patterns)
    Example block output

    Looking at the solution

    Let's see how many of each column we need:

    solution = DataFrames.DataFrame([
+  [17]  =  1

    Let's have a look at the patterns now:

    plot_patterns(data, patterns)
    Example block output

    Looking at the solution

    Let's see how many of each column we need:

    solution = DataFrames.DataFrame([
     (pattern = p, rolls = value(x_p)) for (p, x_p) in enumerate(x)
 ])
 filter!(row -> row.rolls > 0, solution)
    16×2 DataFrame
    Rowpatternrolls
    Int64Float64
    1138.0
    2244.0
    3330.0
    4210.5
    52210.2
    62314.65
    72423.1
    82511.25
    92621.35
    10284.3
    112919.55
    123011.25
    133117.45
    143336.0
    153411.4
    163541.0

    Since we solved a linear program, some of our columns have fractional solutions. We can create a integer feasible solution by rounding up the orders. This requires 341 rolls:

    sum(ceil.(Int, solution.rolls))
    341

    Alternatively, we can re-introduce the integrality constraints and resolve the problem:

    set_integer.(x)
@@ -294,4 +294,4 @@
 solution = DataFrames.DataFrame([
     (pattern = p, rolls = value(x_p)) for (p, x_p) in enumerate(x)
 ])
-filter!(row -> row.rolls > 0, solution)
    16×2 DataFrame
    Rowpatternrolls
    Int64Float64
    1138.0
    2244.0
    3330.0
    4211.0
    5229.0
    62319.0
    72419.0
    82513.0
    92617.0
    10282.0
    112919.0
    123013.0
    133118.0
    143336.0
    153415.0
    163541.0

    This now requires 334 rolls:

    sum(solution.rolls)
    333.99999999999994

    Note that this may not be the global minimum because we are not adding new columns during the solution of the mixed-integer problem model (an algorithm known as branch and price). Nevertheless, the column generation algorithm typically finds good integer feasible solutions to an otherwise intractable optimization problem.

    Next steps

    • Our objective function is to minimize the total number of rolls. What is the total length of waste? How does that compare to the total demand?
    • Writing the optimization algorithm is only part of the challenge. Can you develop a better way to communicate the solution to stakeholders?
    +filter!(row -> row.rolls > 0, solution)
    16×2 DataFrame
    Rowpatternrolls
    Int64Float64
    1138.0
    2244.0
    3330.0
    4211.0
    5229.0
    62319.0
    72419.0
    82513.0
    92617.0
    10282.0
    112919.0
    123013.0
    133118.0
    143336.0
    153415.0
    163541.0

    This now requires 334 rolls:

    sum(solution.rolls)
    333.99999999999994

    Note that this may not be the global minimum because we are not adding new columns during the solution of the mixed-integer problem model (an algorithm known as branch and price). Nevertheless, the column generation algorithm typically finds good integer feasible solutions to an otherwise intractable optimization problem.

    Next steps

    • Our objective function is to minimize the total number of rolls. What is the total length of waste? How does that compare to the total demand?
    • Writing the optimization algorithm is only part of the challenge. Can you develop a better way to communicate the solution to stakeholders?
    diff --git a/previews/PR3913/tutorials/algorithms/parallelism/index.html b/previews/PR3913/tutorials/algorithms/parallelism/index.html index 2f284c266a0..81d466e2567 100644 --- a/previews/PR3913/tutorials/algorithms/parallelism/index.html +++ b/previews/PR3913/tutorials/algorithms/parallelism/index.html @@ -177,4 +177,4 @@ model = Model(Gurobi.Optimizer) set_attribute(model, MOI.NumberOfThreads(), 4)

    GPU parallelism

    JuMP does not support GPU programming, but some solvers support execution on a GPU.

    One example is SCS.jl, which supports using a GPU to internally solve a system of linear equations. If you are on x86_64 Linux machine, do:

    using JuMP, SCS, SCS_GPU_jll
 model = Model(SCS.Optimizer)
-set_attribute(model, "linear_solver", SCS.GpuIndirectSolver)
    +set_attribute(model, "linear_solver", SCS.GpuIndirectSolver) diff --git a/previews/PR3913/tutorials/algorithms/pdhg/index.html b/previews/PR3913/tutorials/algorithms/pdhg/index.html index 024218dbde1..a98f43abadc 100644 --- a/previews/PR3913/tutorials/algorithms/pdhg/index.html +++ b/previews/PR3913/tutorials/algorithms/pdhg/index.html @@ -314,7 +314,7 @@ c3 : [-1.93193e-06,2.50002e-01,1.50000e+00] * Work counters - Solve time (sec) : 2.15682e-01 + Solve time (sec) : 2.10877e-01 Barrier iterations : 8365

    But we could also have written:

    model = Model(Optimizer)
 @variable(model, x >= 0)
@@ -352,7 +352,7 @@
     c2 : 1.50000e+00
 
 * Work counters
-  Solve time (sec)   : 1.75595e-03
+  Solve time (sec)   : 1.74499e-03
   Barrier iterations : 8365

    Other variations are also possible:

    model = Model(Optimizer)
 @variable(model, x[1:5] >= 0)
@@ -390,6 +390,6 @@
     c4 : multiple constraints with the same name
 
 * Work counters
-  Solve time (sec)   : 1.78480e-03
+  Solve time (sec)   : 1.67394e-03
   Barrier iterations : 8365
-

    Behind the scenes, JuMP and MathOptInterface reformulate the problem from the modeller's form into the standard form defined by our Optimizer.

    +

    Behind the scenes, JuMP and MathOptInterface reformulate the problem from the modeller's form into the standard form defined by our Optimizer.

    diff --git a/previews/PR3913/tutorials/algorithms/rolling_horizon/b7eca051.svg b/previews/PR3913/tutorials/algorithms/rolling_horizon/10c2f496.svg similarity index 87% rename from previews/PR3913/tutorials/algorithms/rolling_horizon/b7eca051.svg rename to previews/PR3913/tutorials/algorithms/rolling_horizon/10c2f496.svg index 998ae0641d1..07fcf980e1b 100644 --- a/previews/PR3913/tutorials/algorithms/rolling_horizon/b7eca051.svg +++ b/previews/PR3913/tutorials/algorithms/rolling_horizon/10c2f496.svg @@ -1,360 +1,360 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/algorithms/rolling_horizon/cd050494.svg b/previews/PR3913/tutorials/algorithms/rolling_horizon/121e9cd2.svg similarity index 86% rename from previews/PR3913/tutorials/algorithms/rolling_horizon/cd050494.svg rename to previews/PR3913/tutorials/algorithms/rolling_horizon/121e9cd2.svg index 1bda164e7a2..16a02e0e106 100644 --- a/previews/PR3913/tutorials/algorithms/rolling_horizon/cd050494.svg +++ b/previews/PR3913/tutorials/algorithms/rolling_horizon/121e9cd2.svg @@ -1,118 +1,118 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/algorithms/rolling_horizon/1fb109f8.svg b/previews/PR3913/tutorials/algorithms/rolling_horizon/b5882ca1.svg similarity index 90% rename from previews/PR3913/tutorials/algorithms/rolling_horizon/1fb109f8.svg rename to previews/PR3913/tutorials/algorithms/rolling_horizon/b5882ca1.svg index 435d7502cb8..6f76d95ee67 100644 --- a/previews/PR3913/tutorials/algorithms/rolling_horizon/1fb109f8.svg +++ b/previews/PR3913/tutorials/algorithms/rolling_horizon/b5882ca1.svg @@ -1,80 +1,80 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/algorithms/rolling_horizon/index.html b/previews/PR3913/tutorials/algorithms/rolling_horizon/index.html index 346fbb7a183..9306ae27341 100644 --- a/previews/PR3913/tutorials/algorithms/rolling_horizon/index.html +++ b/previews/PR3913/tutorials/algorithms/rolling_horizon/index.html @@ -29,7 +29,7 @@ xticks = 0:12:total_time_length, xlabel = "Hours", ylabel = "MW", -)Example block output

    JuMP model

    We have all the information we need to create a JuMP model to solve a single window of our rolling horizon problem.

    As the optimizer, we use POI.Optimizer, which is part of ParametricOptInterface.jl. POI.Optimizer converts the Parameter decision variables into constants in the underlying optimization model, and it efficiently updates the solver in-place when we call set_parameter_value which avoids having to rebuild the problem each time we call optimize!.

    model = Model(() -> POI.Optimizer(HiGHS.Optimizer()))
+)
    Example block output

    JuMP model

    We have all the information we need to create a JuMP model to solve a single window of our rolling horizon problem.

    As the optimizer, we use POI.Optimizer, which is part of ParametricOptInterface.jl. POI.Optimizer converts the Parameter decision variables into constants in the underlying optimization model, and it efficiently updates the solver in-place when we call set_parameter_value which avoids having to rebuild the problem each time we call optimize!.

    model = Model(() -> POI.Optimizer(HiGHS.Optimizer()))
 set_silent(model)
 @variables(model, begin
     0 <= r[1:optimization_window]
@@ -118,4 +118,4 @@
     layout = (length(sol_windows), 1),
     size = (600, 800),
     margin = 3Plots.mm,
-)
    Example block output

    We can re-use the function to plot the recovered solution of the full problem:

    plot_solution(sol_complete; offset = 0, xlabel = "Hour")
    Example block output

    Final remark

    ParametricOptInterface.jl offers an easy way to update the parameters of an optimization problem that will be solved several times, as in the rolling horizon implementation. It has the benefit of avoiding rebuilding the model each time we want to solve it with new information in a new window.

    +)Example block output

    We can re-use the function to plot the recovered solution of the full problem:

    plot_solution(sol_complete; offset = 0, xlabel = "Hour")
    Example block output

    Final remark

    ParametricOptInterface.jl offers an easy way to update the parameters of an optimization problem that will be solved several times, as in the rolling horizon implementation. It has the benefit of avoiding rebuilding the model each time we want to solve it with new information in a new window.

    diff --git a/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/18c34496.svg b/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/0c3aa301.svg similarity index 72% rename from previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/18c34496.svg rename to previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/0c3aa301.svg index a8303e0a537..62f2693ea39 100644 --- a/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/18c34496.svg +++ b/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/0c3aa301.svg @@ -1,242 +1,242 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/6412e860.svg b/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/a2c31288.svg similarity index 72% rename from previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/6412e860.svg rename to previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/a2c31288.svg index 5eeb14ed8b4..4a6a260ea69 100644 --- a/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/6412e860.svg +++ b/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/a2c31288.svg @@ -1,242 +1,242 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/index.html b/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/index.html index 36c523e3802..1cbb5ccde0a 100644 --- a/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/index.html +++ b/previews/PR3913/tutorials/algorithms/tsp_lazy_constraints/index.html @@ -97,7 +97,7 @@ Found cycle of length 22 Found cycle of length 3 Found cycle of length 5 -Found cycle of length 21
    objective_value(iterative_model)
    744.6016576596794
    time_iterated
    4.166288137435913

    As a quick sanity check, we visualize the optimal tour to verify that no subtour is present:

    function plot_tour(X, Y, x)
+Found cycle of length 21
    objective_value(iterative_model)
    744.6016576596794
    time_iterated
    4.096730947494507

    As a quick sanity check, we visualize the optimal tour to verify that no subtour is present:

    function plot_tour(X, Y, x)
     plot = Plots.plot()
     for (i, j) in selected_edges(x, size(x, 1))
         Plots.plot!([X[i], X[j]], [Y[i], Y[j]]; legend = false)
@@ -105,7 +105,7 @@
     return plot
 end
 
-plot_tour(X, Y, value.(iterative_model[:x]))
    Example block output

    Lazy constraint method

    A more sophisticated approach makes use of lazy constraints. To be more precise, we do this through the subtour_elimination_callback() below, which is only run whenever we encounter a new integer-feasible solution.

    lazy_model = build_tsp_model(d, n)
+plot_tour(X, Y, value.(iterative_model[:x]))
    Example block output

    Lazy constraint method

    A more sophisticated approach makes use of lazy constraints. To be more precise, we do this through the subtour_elimination_callback() below, which is only run whenever we encounter a new integer-feasible solution.

    lazy_model = build_tsp_model(d, n)
 function subtour_elimination_callback(cb_data)
     status = callback_node_status(cb_data, lazy_model)
     if status != MOI.CALLBACK_NODE_STATUS_INTEGER
@@ -132,4 +132,4 @@
 Set parameter LicenseID to value 722777
 Set parameter GURO_PAR_SPECIAL
 WLS license 722777 - registered to JuMP Development
    @assert is_solved_and_feasible(lazy_model)
-objective_value(lazy_model)
    744.6016576596794
    time_lazy = solve_time(lazy_model)
    2.1133909225463867

    This finds the same optimal tour:

    plot_tour(X, Y, value.(lazy_model[:x]))
    Example block output

    The solution time is faster than the iterative approach:

    Test.@test time_lazy < time_iterated
    Test Passed
    +objective_value(lazy_model)
    744.6016576596794
    time_lazy = solve_time(lazy_model)
    2.038374185562134

    This finds the same optimal tour:

    plot_tour(X, Y, value.(lazy_model[:x]))
    Example block output

    The solution time is faster than the iterative approach:

    Test.@test time_lazy < time_iterated
    Test Passed
    diff --git a/previews/PR3913/tutorials/applications/optimal_power_flow/index.html b/previews/PR3913/tutorials/applications/optimal_power_flow/index.html index 16180e58dd2..6962df679fe 100644 --- a/previews/PR3913/tutorials/applications/optimal_power_flow/index.html +++ b/previews/PR3913/tutorials/applications/optimal_power_flow/index.html @@ -129,7 +129,7 @@ Objective value : 3.08784e+03 * Work counters - Solve time (sec) : 5.45096e-03 + Solve time (sec) : 5.37205e-03 Barrier iterations : 16 
    objval_solution = round(objective_value(model); digits = 2)
 println("Objective value (feasible solution) : $(objval_solution)")
    Objective value (feasible solution) : 3087.84

    The solution's power generation (in rectangular form) and complex voltage values (in polar form using degrees) are:

    DataFrames.DataFrame(;
@@ -215,7 +215,7 @@
   9   1.5653e+03   1.5641e+03  7.67e-04  2.80e-08  3.75e-06  5.96e-03  1.74e-02  4.38e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 61.7ms
    Test.@test is_solved_and_feasible(model; allow_almost = true)
+solve time =  133ms
    Test.@test is_solved_and_feasible(model; allow_almost = true)
 sdp_relaxation_lower_bound = round(objective_value(model); digits = 2)
 println(
     "Objective value (W & V relax. lower bound): $sdp_relaxation_lower_bound",
@@ -232,4 +232,4 @@
     Bus = 1:N,
     Magnitude = round.(abs.(value.(V)); digits = 2),
     AngleDeg = round.(rad2deg.(angle.(value.(V))); digits = 2),
-)
    9×3 DataFrame
    RowBusMagnitudeAngleDeg
    Int64Float64Float64
    110.95-0.0
    220.843.76
    330.832.66
    440.85-1.22
    550.86-2.12
    660.860.93
    770.86-0.18
    880.861.14
    990.85-2.47

    For further information on exploiting sparsity see (Jabr, 2012).

    This relaxation has the advantage that we can work directly with complex voltages to extend the formulation, strengthen the relaxation and gain additional approximate information about the voltage variables.

    +)
    9×3 DataFrame
    RowBusMagnitudeAngleDeg
    Int64Float64Float64
    110.95-0.0
    220.843.76
    330.832.66
    440.85-1.22
    550.86-2.12
    660.860.93
    770.86-0.18
    880.861.14
    990.85-2.47

    For further information on exploiting sparsity see (Jabr, 2012).

    This relaxation has the advantage that we can work directly with complex voltages to extend the formulation, strengthen the relaxation and gain additional approximate information about the voltage variables.

    diff --git a/previews/PR3913/tutorials/applications/power_systems/1effff4a.svg b/previews/PR3913/tutorials/applications/power_systems/75ade8a1.svg similarity index 86% rename from previews/PR3913/tutorials/applications/power_systems/1effff4a.svg rename to previews/PR3913/tutorials/applications/power_systems/75ade8a1.svg index f96f59fddcd..7f8ea189168 100644 --- a/previews/PR3913/tutorials/applications/power_systems/1effff4a.svg +++ b/previews/PR3913/tutorials/applications/power_systems/75ade8a1.svg @@ -1,78 +1,78 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/applications/power_systems/7fb7d857.svg b/previews/PR3913/tutorials/applications/power_systems/89a6126d.svg similarity index 85% rename from previews/PR3913/tutorials/applications/power_systems/7fb7d857.svg rename to previews/PR3913/tutorials/applications/power_systems/89a6126d.svg index 222e038e859..2ba7b451b7f 100644 --- a/previews/PR3913/tutorials/applications/power_systems/7fb7d857.svg +++ b/previews/PR3913/tutorials/applications/power_systems/89a6126d.svg @@ -1,43 +1,43 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/applications/power_systems/5f59aa73.svg b/previews/PR3913/tutorials/applications/power_systems/ce91252c.svg similarity index 86% rename from previews/PR3913/tutorials/applications/power_systems/5f59aa73.svg rename to previews/PR3913/tutorials/applications/power_systems/ce91252c.svg index dbfd630ae0f..596e71fc37a 100644 --- a/previews/PR3913/tutorials/applications/power_systems/5f59aa73.svg +++ b/previews/PR3913/tutorials/applications/power_systems/ce91252c.svg @@ -1,80 +1,80 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/applications/power_systems/index.html b/previews/PR3913/tutorials/applications/power_systems/index.html index 383317d0c5c..30aaf885eb3 100644 --- a/previews/PR3913/tutorials/applications/power_systems/index.html +++ b/previews/PR3913/tutorials/applications/power_systems/index.html @@ -98,7 +98,7 @@ (c_g1_scale, sol.g[1], sol.g[2], sol.w, sol.wind_spill, sol.total_cost), ) end -print(string("elapsed time: ", time() - start, " seconds"))
    elapsed time: 0.17028188705444336 seconds
    c_g_scale_df
    26×6 DataFrame
    Rowscaledispatch_G1dispatch_G2dispatch_windspillage_windtotal_cost
    Float64Float64Float64Float64Float64Float64
    10.51000.0300.0200.00.065000.0
    20.61000.0300.0200.00.070000.0
    30.71000.0300.0200.00.075000.0
    40.81000.0300.0200.00.080000.0
    50.91000.0300.0200.00.085000.0
    61.01000.0300.0200.00.090000.0
    71.11000.0300.0200.00.095000.0
    81.21000.0300.0200.00.0100000.0
    91.31000.0300.0200.00.0105000.0
    101.41000.0300.0200.00.0110000.0
    111.51000.0300.0200.00.0115000.0
    121.61000.0300.0200.00.0120000.0
    131.71000.0300.0200.00.0125000.0
    141.81000.0300.0200.00.0130000.0
    151.91000.0300.0200.00.0135000.0
    162.0300.01000.0200.00.0140000.0
    172.1300.01000.0200.00.0141500.0
    182.2300.01000.0200.00.0143000.0
    192.3300.01000.0200.00.0144500.0
    202.4300.01000.0200.00.0146000.0
    212.5300.01000.0200.00.0147500.0
    222.6300.01000.0200.00.0149000.0
    232.7300.01000.0200.00.0150500.0
    242.8300.01000.0200.00.0152000.0
    252.9300.01000.0200.00.0153500.0
    263.0300.01000.0200.00.0155000.0

    Modifying the JuMP model in-place

    Note that in the previous exercise we entirely rebuilt the optimization model at every iteration of the internal loop, which incurs an additional computational burden. This burden can be alleviated if instead of re-building the entire model, we modify the constraints or objective function, as it shown in the example below.

    Compare the computing time in case of the above and below models.

    function solve_economic_dispatch_inplace(
+print(string("elapsed time: ", time() - start, " seconds"))
    elapsed time: 0.16886281967163086 seconds
    c_g_scale_df
    26×6 DataFrame
    Rowscaledispatch_G1dispatch_G2dispatch_windspillage_windtotal_cost
    Float64Float64Float64Float64Float64Float64
    10.51000.0300.0200.00.065000.0
    20.61000.0300.0200.00.070000.0
    30.71000.0300.0200.00.075000.0
    40.81000.0300.0200.00.080000.0
    50.91000.0300.0200.00.085000.0
    61.01000.0300.0200.00.090000.0
    71.11000.0300.0200.00.095000.0
    81.21000.0300.0200.00.0100000.0
    91.31000.0300.0200.00.0105000.0
    101.41000.0300.0200.00.0110000.0
    111.51000.0300.0200.00.0115000.0
    121.61000.0300.0200.00.0120000.0
    131.71000.0300.0200.00.0125000.0
    141.81000.0300.0200.00.0130000.0
    151.91000.0300.0200.00.0135000.0
    162.0300.01000.0200.00.0140000.0
    172.1300.01000.0200.00.0141500.0
    182.2300.01000.0200.00.0143000.0
    192.3300.01000.0200.00.0144500.0
    202.4300.01000.0200.00.0146000.0
    212.5300.01000.0200.00.0147500.0
    222.6300.01000.0200.00.0149000.0
    232.7300.01000.0200.00.0150500.0
    242.8300.01000.0200.00.0152000.0
    252.9300.01000.0200.00.0153500.0
    263.0300.01000.0200.00.0155000.0

    Modifying the JuMP model in-place

    Note that in the previous exercise we entirely rebuilt the optimization model at every iteration of the internal loop, which incurs an additional computational burden. This burden can be alleviated if instead of re-building the entire model, we modify the constraints or objective function, as it shown in the example below.

    Compare the computing time in case of the above and below models.

    function solve_economic_dispatch_inplace(
     generators::Vector,
     wind,
     scenario,
@@ -155,7 +155,7 @@
     scenario,
     0.5:0.1:3.0,
 )
-print(string("elapsed time: ", time() - start, " seconds"))
    elapsed time: 0.17975997924804688 seconds

    For small models, adjusting specific constraints or the objective function is sometimes faster and sometimes slower than re-building the entire model. However, as the problem size increases, updating the model in-place is usually faster.

    inplace_df
    26×6 DataFrame
    Rowscaledispatch_G1dispatch_G2dispatch_windspillage_windtotal_cost
    Float64Float64Float64Float64Float64Float64
    10.51000.0300.0200.00.065000.0
    20.61000.0300.0200.00.070000.0
    30.71000.0300.0200.00.075000.0
    40.81000.0300.0200.00.080000.0
    50.91000.0300.0200.00.085000.0
    61.01000.0300.0200.00.090000.0
    71.11000.0300.0200.00.095000.0
    81.21000.0300.0200.00.0100000.0
    91.31000.0300.0200.00.0105000.0
    101.41000.0300.0200.00.0110000.0
    111.51000.0300.0200.00.0115000.0
    121.61000.0300.0200.00.0120000.0
    131.71000.0300.0200.00.0125000.0
    141.81000.0300.0200.00.0130000.0
    151.91000.0300.0200.00.0135000.0
    162.01000.0300.0200.00.0140000.0
    172.1300.01000.0200.00.0141500.0
    182.2300.01000.0200.00.0143000.0
    192.3300.01000.0200.00.0144500.0
    202.4300.01000.0200.00.0146000.0
    212.5300.01000.0200.00.0147500.0
    222.6300.01000.0200.00.0149000.0
    232.7300.01000.0200.00.0150500.0
    242.8300.01000.0200.00.0152000.0
    252.9300.01000.0200.00.0153500.0
    263.0300.01000.0200.00.0155000.0

    Inefficient usage of wind generators

    The economic dispatch problem does not perform commitment decisions and, thus, assumes that all generators must be dispatched at least at their minimum power output limit. This approach is not cost efficient and may lead to absurd decisions. For example, if $d = \sum_{i \in I} g^{\min}_{i}$, the wind power injection must be zero, that is, all available wind generation is spilled, to meet the minimum power output constraints on generators.

    In the following example, we adjust the total demand and observed how it affects wind spillage.

    demand_scale_df = DataFrames.DataFrame(;
+print(string("elapsed time: ", time() - start, " seconds"))
    elapsed time: 0.17584800720214844 seconds

    For small models, adjusting specific constraints or the objective function is sometimes faster and sometimes slower than re-building the entire model. However, as the problem size increases, updating the model in-place is usually faster.

    inplace_df
    26×6 DataFrame
    Rowscaledispatch_G1dispatch_G2dispatch_windspillage_windtotal_cost
    Float64Float64Float64Float64Float64Float64
    10.51000.0300.0200.00.065000.0
    20.61000.0300.0200.00.070000.0
    30.71000.0300.0200.00.075000.0
    40.81000.0300.0200.00.080000.0
    50.91000.0300.0200.00.085000.0
    61.01000.0300.0200.00.090000.0
    71.11000.0300.0200.00.095000.0
    81.21000.0300.0200.00.0100000.0
    91.31000.0300.0200.00.0105000.0
    101.41000.0300.0200.00.0110000.0
    111.51000.0300.0200.00.0115000.0
    121.61000.0300.0200.00.0120000.0
    131.71000.0300.0200.00.0125000.0
    141.81000.0300.0200.00.0130000.0
    151.91000.0300.0200.00.0135000.0
    162.01000.0300.0200.00.0140000.0
    172.1300.01000.0200.00.0141500.0
    182.2300.01000.0200.00.0143000.0
    192.3300.01000.0200.00.0144500.0
    202.4300.01000.0200.00.0146000.0
    212.5300.01000.0200.00.0147500.0
    222.6300.01000.0200.00.0149000.0
    232.7300.01000.0200.00.0150500.0
    242.8300.01000.0200.00.0152000.0
    252.9300.01000.0200.00.0153500.0
    263.0300.01000.0200.00.0155000.0

    Inefficient usage of wind generators

    The economic dispatch problem does not perform commitment decisions and, thus, assumes that all generators must be dispatched at least at their minimum power output limit. This approach is not cost efficient and may lead to absurd decisions. For example, if $d = \sum_{i \in I} g^{\min}_{i}$, the wind power injection must be zero, that is, all available wind generation is spilled, to meet the minimum power output constraints on generators.

    In the following example, we adjust the total demand and observed how it affects wind spillage.

    demand_scale_df = DataFrames.DataFrame(;
     demand = Float64[],
     dispatch_G1 = Float64[],
     dispatch_G2 = Float64[],
@@ -212,7 +212,7 @@
     ),
 )
 
-Plots.plot(dispatch_plot, wind_plot)
    Example block output

    This particular drawback can be overcome by introducing binary decisions on the "on/off" status of generators. This model is called unit commitment and considered later in these notes.

    For further reading on the interplay between wind generation and the minimum power output constraints of generators, we refer interested readers to R. Baldick, "Wind and energy markets: a case study of Texas," IEEE Systems Journal, vol. 6, pp. 27-34, 2012.

    Unit commitment

    The Unit Commitment (UC) model can be obtained from ED model by introducing binary variable associated with each generator. This binary variable can attain two values: if it is "1," the generator is synchronized and, thus, can be dispatched, otherwise, that is, if the binary variable is "0," that generator is not synchronized and its power output is set to 0.

    To obtain the mathematical formulation of the UC model, we will modify the constraints of the ED model as follows:

    \[g^{\min}_{i} \cdot u_{t,i} \leq g_{i} \leq g^{\max}_{i} \cdot u_{t,i},\]

    where $u_{i} \in \{0,1\}.$ In this constraint, if $u_{i} = 0$, then $g_{i} = 0$. On the other hand, if $u_{i} = 1$, then $g^{min}_{i} \leq g_{i} \leq g^{max}_{i}$.

    For further reading on the UC problem we refer interested readers to G. Morales-Espana, J. M. Latorre, and A. Ramos, "Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem," IEEE Transactions on Power Systems, vol. 28, pp. 4897-4908, 2013.

    In the following example we convert the ED model explained above to the UC model.

    function solve_unit_commitment(generators::Vector, wind, scenario)
+Plots.plot(dispatch_plot, wind_plot)
    Example block output

    This particular drawback can be overcome by introducing binary decisions on the "on/off" status of generators. This model is called unit commitment and considered later in these notes.

    For further reading on the interplay between wind generation and the minimum power output constraints of generators, we refer interested readers to R. Baldick, "Wind and energy markets: a case study of Texas," IEEE Systems Journal, vol. 6, pp. 27-34, 2012.

    Unit commitment

    The Unit Commitment (UC) model can be obtained from ED model by introducing binary variable associated with each generator. This binary variable can attain two values: if it is "1," the generator is synchronized and, thus, can be dispatched, otherwise, that is, if the binary variable is "0," that generator is not synchronized and its power output is set to 0.

    To obtain the mathematical formulation of the UC model, we will modify the constraints of the ED model as follows:

    \[g^{\min}_{i} \cdot u_{t,i} \leq g_{i} \leq g^{\max}_{i} \cdot u_{t,i},\]

    where $u_{i} \in \{0,1\}.$ In this constraint, if $u_{i} = 0$, then $g_{i} = 0$. On the other hand, if $u_{i} = 1$, then $g^{min}_{i} \leq g_{i} \leq g^{max}_{i}$.

    For further reading on the UC problem we refer interested readers to G. Morales-Espana, J. M. Latorre, and A. Ramos, "Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem," IEEE Transactions on Power Systems, vol. 28, pp. 4897-4908, 2013.

    In the following example we convert the ED model explained above to the UC model.

    function solve_unit_commitment(generators::Vector, wind, scenario)
     model = Model(HiGHS.Optimizer)
     set_silent(model)
     N = length(generators)
@@ -325,7 +325,7 @@
     ),
 )
 
-Plots.plot(commitment_plot, dispatch_plot)
    Example block output

    Nonlinear economic dispatch

    As a final example, we modify our economic dispatch problem in two ways:

    • The thermal cost function is user-defined
    • The output of the wind is only the square-root of the dispatch
    import Ipopt
+Plots.plot(commitment_plot, dispatch_plot)
    Example block output

    Nonlinear economic dispatch

    As a final example, we modify our economic dispatch problem in two ways:

    • The thermal cost function is user-defined
    • The output of the wind is only the square-root of the dispatch
    import Ipopt
 
 """
     thermal_cost_function(g)
@@ -395,4 +395,4 @@
     xlabel = "Cost",
     ylabel = "Dispatch [MW]",
     label = false,
-)
    Example block output +)Example block output diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/048f5528.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/048f5528.svg new file mode 100644 index 00000000000..25d3b6e140e --- /dev/null +++ b/previews/PR3913/tutorials/applications/two_stage_stochastic/048f5528.svg @@ -0,0 +1,130 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/0d0ebf54.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/0d0ebf54.svg new file mode 100644 index 00000000000..5532616f5c6 --- /dev/null +++ b/previews/PR3913/tutorials/applications/two_stage_stochastic/0d0ebf54.svg @@ -0,0 +1,93 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/215ff7c1.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/215ff7c1.svg deleted file mode 100644 index c6c5b555a87..00000000000 --- a/previews/PR3913/tutorials/applications/two_stage_stochastic/215ff7c1.svg +++ /dev/null @@ -1,73 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/299a251d.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/299a251d.svg deleted file mode 100644 index efd56776de4..00000000000 --- a/previews/PR3913/tutorials/applications/two_stage_stochastic/299a251d.svg +++ /dev/null @@ -1,102 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/3fdcc408.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/3fdcc408.svg new file mode 100644 index 00000000000..c24fba5a860 --- /dev/null +++ b/previews/PR3913/tutorials/applications/two_stage_stochastic/3fdcc408.svg @@ -0,0 +1,89 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/a0085235.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/a0085235.svg deleted file mode 100644 index f7607a07ba0..00000000000 --- a/previews/PR3913/tutorials/applications/two_stage_stochastic/a0085235.svg +++ /dev/null @@ -1,99 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/ac1a4494.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/ac1a4494.svg new file mode 100644 index 00000000000..438d38373b0 --- /dev/null +++ b/previews/PR3913/tutorials/applications/two_stage_stochastic/ac1a4494.svg @@ -0,0 +1,105 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/d21f542e.svg b/previews/PR3913/tutorials/applications/two_stage_stochastic/d21f542e.svg deleted file mode 100644 index 4fd68dc92ab..00000000000 --- a/previews/PR3913/tutorials/applications/two_stage_stochastic/d21f542e.svg +++ /dev/null @@ -1,77 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/previews/PR3913/tutorials/applications/two_stage_stochastic/index.html b/previews/PR3913/tutorials/applications/two_stage_stochastic/index.html index 9e673f87746..04d4be1e0b8 100644 --- a/previews/PR3913/tutorials/applications/two_stage_stochastic/index.html +++ b/previews/PR3913/tutorials/applications/two_stage_stochastic/index.html @@ -18,7 +18,7 @@ d = sort!(rand(D, N)); Ω = 1:N P = fill(1 / N, N); -StatsPlots.histogram(d; bins = 20, label = "", xlabel = "Demand")Example block output

    JuMP model

    The implementation of our two-stage stochastic program in JuMP is:

    model = Model(HiGHS.Optimizer)
+StatsPlots.histogram(d; bins = 20, label = "", xlabel = "Demand")
    Example block output

    JuMP model

    The implementation of our two-stage stochastic program in JuMP is:

    model = Model(HiGHS.Optimizer)
 set_silent(model)
 @variable(model, x >= 0)
 @variable(model, 0 <= y[ω in Ω] <= d[ω])
@@ -38,37 +38,37 @@
 * Candidate solution (result #1)
   Primal status      : FEASIBLE_POINT
   Dual status        : FEASIBLE_POINT
-  Objective value    : 5.50021e+02
-  Objective bound    : 5.50021e+02
-  Relative gap       : 2.06695e-16
-  Dual objective value : 5.50021e+02
+  Objective value    : 5.71196e+02
+  Objective bound    : 5.71196e+02
+  Relative gap       : 9.95164e-16
+  Dual objective value : 5.71196e+02
 
 * Work counters
-  Solve time (sec)   : 3.71456e-04
+  Solve time (sec)   : 3.51667e-04
   Simplex iterations : 42
   Barrier iterations : 0
   Node count         : -1
-

    The optimal number of pies to make is:

    value(x)
    201.89659831000657

    The distribution of total profit is:

    total_profit = [-2 * value(x) + value(z[ω]) for ω in Ω]
    100-element Vector{Float64}:
- 405.4353685691771
- 412.9715920029268
- 421.7679787727125
- 427.3138371618473
- 427.41784539401925
- 429.7319135759894
- 434.571437004516
- 438.3784152127069
- 438.79067768888837
- 443.64300201018153
+

    The optimal number of pies to make is:

    value(x)
    208.73415338263257

    The distribution of total profit is:

    total_profit = [-2 * value(x) + value(z[ω]) for ω in Ω]
    100-element Vector{Float64}:
+ 332.9216855334716
+ 388.27103683631725
+ 422.6223799359039
+ 422.7281743431403
+ 423.6855089499142
+ 432.63120338888126
+ 445.49200224714804
+ 470.7573619320271
+ 470.92186689259194
+ 480.8341813992874
    ⋮
- 605.6897949300196
- 605.6897949300196
- 605.6897949300196
- 605.6897949300196
- 605.6897949300196
- 605.6897949300196
- 605.6897949300196
- 605.6897949300196
- 605.6897949300196

    Let's plot it:

    """
+ 626.2024601478977
+ 626.2024601478977
+ 626.2024601478977
+ 626.2024601478977
+ 626.2024601478977
+ 626.2024601478977
+ 626.2024601478977
+ 626.2024601478977
+ 626.2024601478977

    Let's plot it:

    """
     bin_distribution(x::Vector{Float64}, N::Int)
 
 A helper function that discretizes `x` into bins of width `N`.
@@ -89,7 +89,7 @@
     label = "Expected profit (\$$(round(Int, μ)))",
     linewidth = 3,
 )
-plot
    Example block output

    Risk measures

    A risk measure is a function which maps a random variable to a real number. Common risk measures include the mean (expectation), median, mode, and maximum. We need a risk measure to convert the distribution of second stage costs into a single number that can be optimized.

    Our model currently uses the expectation risk measure, but others are possible too. One popular risk measure is the conditional value at risk (CVaR).

    CVaR has a parameter $\gamma$, and it computes the expectation of the worst $\gamma$ fraction of outcomes.

    If we are maximizing, so that small outcomes are bad, the definition of CVaR is:

    \[CVaR_{\gamma}[Z] = \max\limits_{\xi} \;\; \xi - \frac{1}{\gamma}\mathbb{E}_\omega\left[(\xi - Z)_+\right]\]

    which can be formulated as the linear program:

    \[\begin{aligned} +plotExample block output

    Risk measures

    A risk measure is a function which maps a random variable to a real number. Common risk measures include the mean (expectation), median, mode, and maximum. We need a risk measure to convert the distribution of second stage costs into a single number that can be optimized.

    Our model currently uses the expectation risk measure, but others are possible too. One popular risk measure is the conditional value at risk (CVaR).

    CVaR has a parameter $\gamma$, and it computes the expectation of the worst $\gamma$ fraction of outcomes.

    If we are maximizing, so that small outcomes are bad, the definition of CVaR is:

    \[CVaR_{\gamma}[Z] = \max\limits_{\xi} \;\; \xi - \frac{1}{\gamma}\mathbb{E}_\omega\left[(\xi - Z)_+\right]\]

    which can be formulated as the linear program:

    \[\begin{aligned} CVaR_{\gamma}[Z] = \max\limits_{\xi, z_\omega} \;\; & \xi - \frac{1}{\gamma}\sum P_\omega z_\omega\\ & z_\omega \ge \xi - Z_\omega & \quad \forall \omega \\ & z_\omega \ge 0 & \quad \forall \omega. @@ -105,7 +105,7 @@ optimize!(model) @assert is_solved_and_feasible(model) return objective_value(model) -end

    CVaR (generic function with 1 method)

    When γ is 1.0, we compute the mean of the profit:

    cvar_10 = CVaR(total_profit, P; γ = 1.0)
    550.0212663461099
    Statistics.mean(total_profit)
    550.0212663461101

    As γ approaches 0.0, we compute the worst-case (minimum) profit:

    cvar_00 = CVaR(total_profit, P; γ = 0.0001)
    405.4353685691771
    minimum(total_profit)
    405.4353685691771

    By varying γ between 0 and 1 we can compute some trade-off of these two extremes:

    cvar_05 = CVaR(total_profit, P; γ = 0.5)
    497.7888085187476

    Let's plot these outcomes on our distribution:

    plot = StatsPlots.histogram(
+end
    CVaR (generic function with 1 method)

    When γ is 1.0, we compute the mean of the profit:

    cvar_10 = CVaR(total_profit, P; γ = 1.0)
    571.1963924209059
    Statistics.mean(total_profit)
    571.1963924209059

    As γ approaches 0.0, we compute the worst-case (minimum) profit:

    cvar_00 = CVaR(total_profit, P; γ = 0.0001)
    332.9216855334716
    minimum(total_profit)
    332.9216855334716

    By varying γ between 0 and 1 we can compute some trade-off of these two extremes:

    cvar_05 = CVaR(total_profit, P; γ = 0.5)
    520.2543866818612

    Let's plot these outcomes on our distribution:

    plot = StatsPlots.histogram(
     total_profit;
     bins = bin_distribution(total_profit, 25),
     label = "",
@@ -118,7 +118,7 @@
     label = ["γ = 1.0" "γ = 0.5" "γ = 0.0"],
     linewidth = 3,
 )
-plot
    Example block output

    Risk averse sample average approximation

    Because CVaR can be formulated as a linear program, we can form a risk averse sample average approximation model by combining the two formulations:

    γ = 0.4
+plot
    Example block output

    Risk averse sample average approximation

    Because CVaR can be formulated as a linear program, we can form a risk averse sample average approximation model by combining the two formulations:

    γ = 0.4
 model = Model(HiGHS.Optimizer)
 set_silent(model)
 @variable(model, x >= 0)
@@ -130,7 +130,7 @@
 @constraint(model, [ω in Ω], z[ω] >= ξ - Z[ω])
 @objective(model, Max, -2x + ξ - 1 / γ * sum(P[ω] * z[ω] for ω in Ω))
 optimize!(model)
-@assert is_solved_and_feasible(model)

    When $\gamma = 0.4$, the optimal number of pies to bake is:

    value(x)
    180.59344489218662

    The distribution of total profit is:

    risk_averse_total_profit = [value(-2x + Z[ω]) for ω in Ω]
+@assert is_solved_and_feasible(model)

    When $\gamma = 0.4$, the optimal number of pies to bake is:

    value(x)
    190.7699246927299

    The distribution of total profit is:

    risk_averse_total_profit = [value(-2x + Z[ω]) for ω in Ω]
 bins = bin_distribution([total_profit; risk_averse_total_profit], 25)
 plot = StatsPlots.histogram(total_profit; label = "Expectation", bins = bins)
 StatsPlots.histogram!(
@@ -140,4 +140,4 @@
     bins = bins,
     alpha = 0.5,
 )
-plot
    Example block output

    Next steps

    • Try solving this problem for different numbers of samples and different distributions.
    • Refactor the example to avoid hard-coding the costs. What happens to the solution if the cost of disposing unsold pies increases?
    • Plot the optimal number of pies to make for different values of the risk aversion parameter $\gamma$. What is the relationship?
    +plotExample block output

    Next steps

    • Try solving this problem for different numbers of samples and different distributions.
    • Refactor the example to avoid hard-coding the costs. What happens to the solution if the cost of disposing unsold pies increases?
    • Plot the optimal number of pies to make for different values of the risk aversion parameter $\gamma$. What is the relationship?
    diff --git a/previews/PR3913/tutorials/applications/web_app/index.html b/previews/PR3913/tutorials/applications/web_app/index.html index a3a697c9a01..2b2790b5dee 100644 --- a/previews/PR3913/tutorials/applications/web_app/index.html +++ b/previews/PR3913/tutorials/applications/web_app/index.html @@ -59,7 +59,7 @@ end end return server -end
    setup_server (generic function with 1 method)
    Warning

    HTTP.jl does not serve requests on a separate thread. Therefore, a long-running job will block the main thread, preventing concurrent users from submitting requests. To work-around this, read HTTP.jl issue 798 or watch Building Microservices and Applications in Julia from JuliaCon 2020.

    server = setup_server(HTTP.ip"127.0.0.1", 8080)
    Sockets.TCPServer(RawFD(38) active)

    The client side

    Now that we have a server, we can send it requests via this function:

    function send_request(data::Dict; endpoint::String = "solve")
+end
    setup_server (generic function with 1 method)
    Warning

    HTTP.jl does not serve requests on a separate thread. Therefore, a long-running job will block the main thread, preventing concurrent users from submitting requests. To work-around this, read HTTP.jl issue 798 or watch Building Microservices and Applications in Julia from JuliaCon 2020.

    server = setup_server(HTTP.ip"127.0.0.1", 8080)
    Sockets.TCPServer(RawFD(36) active)

    The client side

    Now that we have a server, we can send it requests via this function:

    function send_request(data::Dict; endpoint::String = "solve")
     ret = HTTP.request(
         "POST",
         # This should match the URL and endpoint we defined for our server.
@@ -88,4 +88,4 @@
   "status" => "failure"
   "reason" => "missing lower_bound param"

    If we don't send a lower_bound that is a number, we get:

    send_request(Dict("lower_bound" => "1.2"))
    Dict{String, Any} with 2 entries:
   "status" => "failure"
-  "reason" => "lower_bound is not a number"

    Finally, we can shutdown our HTTP server:

    close(server)
    [ Info: Server on 127.0.0.1:8080 closing

    Next steps

    For more complicated examples relating to HTTP servers, consult the HTTP.jl documentation.

    To see how you can integrate this with a larger JuMP model, read Design patterns for larger models.

    + "reason" => "lower_bound is not a number"

    Finally, we can shutdown our HTTP server:

    close(server)
    [ Info: Server on 127.0.0.1:8080 closing

    Next steps

    For more complicated examples relating to HTTP servers, consult the HTTP.jl documentation.

    To see how you can integrate this with a larger JuMP model, read Design patterns for larger models.

    diff --git a/previews/PR3913/tutorials/conic/arbitrary_precision/index.html b/previews/PR3913/tutorials/conic/arbitrary_precision/index.html index 0b5da4ff0b9..a4af7e08e3c 100644 --- a/previews/PR3913/tutorials/conic/arbitrary_precision/index.html +++ b/previews/PR3913/tutorials/conic/arbitrary_precision/index.html @@ -37,7 +37,7 @@ Dual objective value : -6.42857e-01 * Work counters - Solve time (sec) : 4.45786e-01 + Solve time (sec) : 4.39864e-01 Barrier iterations : 5

    The value of each decision variable is a BigFloat:

    value.(x)
    2-element Vector{BigFloat}:
  0.4285714246558161076147072906813123533593766450416896337912086518811186790735189
@@ -82,4 +82,4 @@
 * Work counters

    The optimal values are given in exact rational arithmetic:

    value.(x)
    2-element Vector{Rational{BigInt}}:
  1//6
- 2//3
    objective_value(model)
    5//6
    value(c2)
    13//6
    + 2//3
    objective_value(model)
    5//6
    value(c2)
    13//6
    diff --git a/previews/PR3913/tutorials/conic/dualization/index.html b/previews/PR3913/tutorials/conic/dualization/index.html index 8dcfae95007..dceae7f0db3 100644 --- a/previews/PR3913/tutorials/conic/dualization/index.html +++ b/previews/PR3913/tutorials/conic/dualization/index.html @@ -53,12 +53,12 @@ ------------------------------------------------------------------ iter | pri res | dua res | gap | obj | scale | time (s) ------------------------------------------------------------------ - 0| 1.65e+01 1.60e-01 5.09e+01 -2.91e+01 1.00e-01 1.05e-04 - 50| 1.74e-08 2.70e-10 4.88e-08 -4.00e+00 1.00e-01 1.84e-04 + 0| 1.65e+01 1.60e-01 5.09e+01 -2.91e+01 1.00e-01 1.18e-03 + 50| 1.74e-08 2.70e-10 4.88e-08 -4.00e+00 1.00e-01 7.18e-03 ------------------------------------------------------------------ status: solved -timings: total: 1.85e-04s = setup: 4.12e-05s + solve: 1.44e-04s - lin-sys: 1.14e-05s, cones: 6.03e-05s, accel: 2.72e-06s +timings: total: 7.18e-03s = setup: 4.12e-05s + solve: 7.14e-03s + lin-sys: 1.13e-05s, cones: 6.94e-05s, accel: 2.76e-06s ------------------------------------------------------------------ objective = -4.000000 ------------------------------------------------------------------

    (There are five rows in the constraint matrix because SCS expects problems in geometric conic form, and so JuMP has reformulated the X, PSD variable constraint into the affine constraint X .+ 0 in PSDCone().)

    The solution we obtain is:

    value.(X)
    2×2 Matrix{Float64}:
@@ -83,12 +83,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.23e+01  1.00e+00  2.73e+01 -9.03e+00  1.00e-01  9.85e-05
-    50| 1.13e-07  1.05e-09  3.23e-07  4.00e+00  1.00e-01  1.81e-04
+     0| 1.23e+01  1.00e+00  2.73e+01 -9.03e+00  1.00e-01  1.02e-04
+    50| 1.13e-07  1.05e-09  3.23e-07  4.00e+00  1.00e-01  1.82e-04
 ------------------------------------------------------------------
 status:  solved
-timings: total: 1.82e-04s = setup: 4.56e-05s + solve: 1.36e-04s
-	 lin-sys: 9.20e-06s, cones: 6.02e-05s, accel: 2.69e-06s
+timings: total: 1.83e-04s = setup: 4.24e-05s + solve: 1.41e-04s
+	 lin-sys: 9.27e-06s, cones: 5.83e-05s, accel: 2.69e-06s
 ------------------------------------------------------------------
 objective = 4.000000
 ------------------------------------------------------------------

    and the solution we obtain is:

    dual.(dual_c)
    2×2 Matrix{Float64}:
@@ -113,12 +113,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.23e+01  1.00e+00  2.73e+01 -9.03e+00  1.00e-01  8.96e-05
-    50| 1.13e-07  1.05e-09  3.23e-07  4.00e+00  1.00e-01  1.71e-04
+     0| 1.23e+01  1.00e+00  2.73e+01 -9.03e+00  1.00e-01  8.94e-05
+    50| 1.13e-07  1.05e-09  3.23e-07  4.00e+00  1.00e-01  1.69e-04
 ------------------------------------------------------------------
 status:  solved
-timings: total: 1.72e-04s = setup: 3.97e-05s + solve: 1.33e-04s
-	 lin-sys: 9.33e-06s, cones: 5.97e-05s, accel: 2.62e-06s
+timings: total: 1.70e-04s = setup: 3.86e-05s + solve: 1.31e-04s
+	 lin-sys: 9.42e-06s, cones: 5.90e-05s, accel: 2.74e-06s
 ------------------------------------------------------------------
 objective = 4.000000
 ------------------------------------------------------------------

    The performance is the same as if we solved model_dual, and the correct solution is returned to X:

    value.(X)
    2×2 Matrix{Float64}:
@@ -144,12 +144,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.65e+01  1.60e-01  5.09e+01 -2.91e+01  1.00e-01  9.76e-05
-    50| 1.74e-08  2.70e-10  4.88e-08 -4.00e+00  1.00e-01  1.75e-04
+     0| 1.65e+01  1.60e-01  5.09e+01 -2.91e+01  1.00e-01  1.73e-03
+    50| 1.74e-08  2.70e-10  4.88e-08 -4.00e+00  1.00e-01  1.81e-03
 ------------------------------------------------------------------
 status:  solved
-timings: total: 1.76e-04s = setup: 4.18e-05s + solve: 1.35e-04s
-	 lin-sys: 1.10e-05s, cones: 5.96e-05s, accel: 2.65e-06s
+timings: total: 1.81e-03s = setup: 4.28e-05s + solve: 1.76e-03s
+	 lin-sys: 1.14e-05s, cones: 5.91e-05s, accel: 2.73e-06s
 ------------------------------------------------------------------
 objective = -4.000000
 ------------------------------------------------------------------
    dual.(dual_c)
    2×2 Matrix{Float64}:
@@ -185,12 +185,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 4.73e+00  1.00e+00  2.92e+00  1.23e+00  1.00e-01  1.28e-04
-   150| 1.01e-04  3.07e-05  6.08e-05  1.33e+00  1.00e-01  7.23e-04
+     0| 4.73e+00  1.00e+00  2.92e+00  1.23e+00  1.00e-01  1.23e-04
+   150| 1.01e-04  3.07e-05  6.08e-05  1.33e+00  1.00e-01  6.86e-04
 ------------------------------------------------------------------
 status:  solved
-timings: total: 7.24e-04s = setup: 6.46e-05s + solve: 6.59e-04s
-	 lin-sys: 1.03e-04s, cones: 4.09e-04s, accel: 3.66e-05s
+timings: total: 6.87e-04s = setup: 6.19e-05s + solve: 6.25e-04s
+	 lin-sys: 1.00e-04s, cones: 3.82e-04s, accel: 3.56e-05s
 ------------------------------------------------------------------
 objective = 1.333363
 ------------------------------------------------------------------
    set_optimizer(model, Dualization.dual_optimizer(SCS.Optimizer))
@@ -212,12 +212,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 3.71e+01  1.48e+00  2.23e+02 -1.13e+02  1.00e-01  1.49e-04
-   150| 1.57e-04  2.28e-05  2.08e-04 -1.33e+00  1.00e-01  7.49e-04
+     0| 3.71e+01  1.48e+00  2.23e+02 -1.13e+02  1.00e-01  1.32e-04
+   150| 1.57e-04  2.28e-05  2.08e-04 -1.33e+00  1.00e-01  7.20e-04
 ------------------------------------------------------------------
 status:  solved
-timings: total: 7.51e-04s = setup: 7.30e-05s + solve: 6.78e-04s
-	 lin-sys: 1.10e-04s, cones: 4.14e-04s, accel: 2.70e-05s
+timings: total: 7.21e-04s = setup: 6.96e-05s + solve: 6.52e-04s
+	 lin-sys: 1.09e-04s, cones: 4.05e-04s, accel: 2.69e-05s
 ------------------------------------------------------------------
 objective = -1.333460
-------------------------------------------------------------------

    For this problem, SCS reports that the primal has variables n: 11, constraints m: 24 and that the dual has variables n: 14, constraints m: 24. Therefore, we should probably use the primal formulation because it has fewer variables and the same number of constraints.

    When to use dual_optimizer

    Because it can make the problem larger or smaller, depending on the problem and the choice of solver, there is no definitive rule on when you should use dual_optimizer. However, you should try dual_optimizer if your conic optimization problem takes a long time to solve, or if you need to repeatedly solve similarly structured problems with different data. In some cases solving the dual instead of the primal can make a large difference.

    +------------------------------------------------------------------

    For this problem, SCS reports that the primal has variables n: 11, constraints m: 24 and that the dual has variables n: 14, constraints m: 24. Therefore, we should probably use the primal formulation because it has fewer variables and the same number of constraints.

    When to use dual_optimizer

    Because it can make the problem larger or smaller, depending on the problem and the choice of solver, there is no definitive rule on when you should use dual_optimizer. However, you should try dual_optimizer if your conic optimization problem takes a long time to solve, or if you need to repeatedly solve similarly structured problems with different data. In some cases solving the dual instead of the primal can make a large difference.

    diff --git a/previews/PR3913/tutorials/conic/ellipse_approx/66a5da6e.svg b/previews/PR3913/tutorials/conic/ellipse_approx/819d86ac.svg similarity index 57% rename from previews/PR3913/tutorials/conic/ellipse_approx/66a5da6e.svg rename to previews/PR3913/tutorials/conic/ellipse_approx/819d86ac.svg index ea860b9f4f7..cae21e25409 100644 --- a/previews/PR3913/tutorials/conic/ellipse_approx/66a5da6e.svg +++ b/previews/PR3913/tutorials/conic/ellipse_approx/819d86ac.svg @@ -1,2443 +1,2443 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/conic/ellipse_approx/index.html b/previews/PR3913/tutorials/conic/ellipse_approx/index.html index 79037dc9861..af1eb928fad 100644 --- a/previews/PR3913/tutorials/conic/ellipse_approx/index.html +++ b/previews/PR3913/tutorials/conic/ellipse_approx/index.html @@ -36,7 +36,7 @@ c = :green, shape = :x, size = (600, 600), -)Example block output

    JuMP formulation

    Now let's build and the JuMP model. We'll compute $D$ and $c$ after the solve.

    model = Model(SCS.Optimizer)
+)
    Example block output

    JuMP formulation

    Now let's build and the JuMP model. We'll compute $D$ and $c$ after the solve.

    model = Model(SCS.Optimizer)
 # We need to use a tighter tolerance for this example, otherwise the bounding
 # ellipse won't actually be bounding...
 set_attribute(model, "eps_rel", 1e-7)
@@ -71,7 +71,7 @@
   Dual objective value : 5.08382e-03
 
 * Work counters
-  Solve time (sec)   : 2.98768e-01
+  Solve time (sec)   : 2.98484e-01

    Results

    After solving the model to optimality we can recover the solution in terms of $D$ and $c$:

    D = value.(Z)
    2×2 Matrix{Float64}:
   0.00755264  -0.0114233
  -0.0114233    0.0206963
    c = D \ value.(z)
    2-element Vector{Float64}:
@@ -79,7 +79,7 @@
  -2.255547187078282

    We can check that each point lies inside the ellipsoid, by checking if the largest normalized radius is less than 1:

    largest_radius = maximum(map(x -> (x - c)' * D * (x - c), eachrow(S)))
    0.999891803944291

    Finally, overlaying the solution in the plot we see the minimal volume approximating ellipsoid:

    P = sqrt(D)
 q = -P * c
 data = [tuple(P \ [cos(θ) - q[1], sin(θ) - q[2]]...) for θ in 0:0.05:(2pi+0.05)]
-Plots.plot!(plot, data; c = :crimson, label = nothing)
    Example block output

    Alternative formulations

    The formulation of model uses MOI.RootDetConeSquare. However, because SCS does not natively support this cone, JuMP automatically reformulates the problem into an equivalent problem that SCS does support. You can see the reformulation that JuMP chose using print_active_bridges:

    print_active_bridges(model)
     * Unsupported objective: MOI.VariableIndex
+Plots.plot!(plot, data; c = :crimson, label = nothing)
    Example block output

    Alternative formulations

    The formulation of model uses MOI.RootDetConeSquare. However, because SCS does not natively support this cone, JuMP automatically reformulates the problem into an equivalent problem that SCS does support. You can see the reformulation that JuMP chose using print_active_bridges:

    print_active_bridges(model)
     * Unsupported objective: MOI.VariableIndex
  |  bridged by:
  |   MOIB.Objective.FunctionConversionBridge{Float64, MOI.ScalarAffineFunction{Float64}, MOI.VariableIndex}
  |  may introduce:
@@ -259,7 +259,7 @@
 @objective(model, Max, 1 * t + 0)
 optimize!(model)
 Test.@test is_solved_and_feasible(model)
-solve_time_1 = solve_time(model)
    0.294549389

    This formulation gives the much smaller graph:

    print_active_bridges(model)
     * Supported objective: MOI.ScalarAffineFunction{Float64}
+solve_time_1 = solve_time(model)
    0.297803416

    This formulation gives the much smaller graph:

    print_active_bridges(model)
     * Supported objective: MOI.ScalarAffineFunction{Float64}
  * Supported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.Nonnegatives
  * Unsupported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.PositiveSemidefiniteConeTriangle
  |  bridged by:
@@ -298,7 +298,7 @@
  |   |   |   |   * Supported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.Nonnegatives
  |   * Supported variable: MOI.Reals

    The last bullet shows how JuMP reformulated the MOI.RootDetConeTriangle constraint by adding a mix of MOI.PositiveSemidefiniteConeTriangle and MOI.GeometricMeanCone constraints.

    Because SCS doesn't natively support the MOI.GeometricMeanCone, these constraints were further bridged using a MOI.Bridges.Constraint.GeoMeanToPowerBridge to a series of MOI.PowerCone constraints.

    However, there are many other ways that a MOI.GeometricMeanCone can be reformulated into something that SCS supports. Let's see what happens if we use remove_bridge to remove the MOI.Bridges.Constraint.GeoMeanToPowerBridge:

    remove_bridge(model, MOI.Bridges.Constraint.GeoMeanToPowerBridge)
 optimize!(model)
-Test.@test is_solved_and_feasible(model)
    Test Passed

    This time, the solve took:

    solve_time_2 = solve_time(model)
    0.289482742

    where previously it took

    solve_time_1
    0.294549389

    Why was the solve time different?

    print_active_bridges(model)
     * Supported objective: MOI.ScalarAffineFunction{Float64}
+Test.@test is_solved_and_feasible(model)
    Test Passed

    This time, the solve took:

    solve_time_2 = solve_time(model)
    0.350935436

    where previously it took

    solve_time_1
    0.297803416

    Why was the solve time different?

    print_active_bridges(model)
     * Supported objective: MOI.ScalarAffineFunction{Float64}
  * Supported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.Nonnegatives
  * Unsupported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.PositiveSemidefiniteConeTriangle
  |  bridged by:
@@ -342,4 +342,4 @@
  |   |   |   * Supported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.SecondOrderCone
  |   |   * Supported constraint: MOI.VectorAffineFunction{Float64}-in-MOI.Nonnegatives
  |   |   * Supported variable: MOI.Reals
- |   * Supported variable: MOI.Reals

    This time, JuMP used a MOI.Bridges.Constraint.GeoMeanBridge to reformulate the constraint into a set of MOI.RotatedSecondOrderCone constraints, which were further reformulated into a set of supported MOI.SecondOrderCone constraints.

    Since the two models are equivalent, we can conclude that for this particular model, the MOI.SecondOrderCone formulation is more efficient.

    In general though, the performance of a particular reformulation is problem- and solver-specific. Therefore, JuMP chooses to minimize the number of bridges in the default reformulation, leaving you to explore alternative formulations using the tools and techniques shown in this tutorial.

    + | * Supported variable: MOI.Reals

    This time, JuMP used a MOI.Bridges.Constraint.GeoMeanBridge to reformulate the constraint into a set of MOI.RotatedSecondOrderCone constraints, which were further reformulated into a set of supported MOI.SecondOrderCone constraints.

    Since the two models are equivalent, we can conclude that for this particular model, the MOI.SecondOrderCone formulation is more efficient.

    In general though, the performance of a particular reformulation is problem- and solver-specific. Therefore, JuMP chooses to minimize the number of bridges in the default reformulation, leaving you to explore alternative formulations using the tools and techniques shown in this tutorial.

    diff --git a/previews/PR3913/tutorials/conic/ellipse_fitting/3ff39ff8.svg b/previews/PR3913/tutorials/conic/ellipse_fitting/2a7deebf.svg similarity index 80% rename from previews/PR3913/tutorials/conic/ellipse_fitting/3ff39ff8.svg rename to previews/PR3913/tutorials/conic/ellipse_fitting/2a7deebf.svg index f86dbb43f68..cab365097b7 100644 --- a/previews/PR3913/tutorials/conic/ellipse_fitting/3ff39ff8.svg +++ b/previews/PR3913/tutorials/conic/ellipse_fitting/2a7deebf.svg @@ -1,35 +1,35 @@ - + - + - + - + - + - - - - - - - - - - - - - + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/conic/ellipse_fitting/053e2c86.svg b/previews/PR3913/tutorials/conic/ellipse_fitting/437667c7.svg similarity index 98% rename from previews/PR3913/tutorials/conic/ellipse_fitting/053e2c86.svg rename to previews/PR3913/tutorials/conic/ellipse_fitting/437667c7.svg index e335c3305b6..aa6de3c1f90 100644 --- a/previews/PR3913/tutorials/conic/ellipse_fitting/053e2c86.svg +++ b/previews/PR3913/tutorials/conic/ellipse_fitting/437667c7.svg @@ -1,49 +1,49 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - + - + - + - + - + - - - - - - - - - - - - - + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/conic/ellipse_fitting/b171446c.svg b/previews/PR3913/tutorials/conic/ellipse_fitting/a5a41812.svg similarity index 80% rename from previews/PR3913/tutorials/conic/ellipse_fitting/b171446c.svg rename to previews/PR3913/tutorials/conic/ellipse_fitting/a5a41812.svg index ca546a81072..6da4876583f 100644 --- a/previews/PR3913/tutorials/conic/ellipse_fitting/b171446c.svg +++ b/previews/PR3913/tutorials/conic/ellipse_fitting/a5a41812.svg @@ -1,35 +1,35 @@ - + - + - + - + - + - - - - - - - - - - - - - + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/conic/ellipse_fitting/index.html b/previews/PR3913/tutorials/conic/ellipse_fitting/index.html index 80b3c1672d2..37a33f97866 100644 --- a/previews/PR3913/tutorials/conic/ellipse_fitting/index.html +++ b/previews/PR3913/tutorials/conic/ellipse_fitting/index.html @@ -74,7 +74,7 @@ Images.mosaicview(x, Images.Gray.(x_final); nrow = 1)Example block output

    We then use a binarization algorithm to map each grayscale pixel $(x_i, y_i)$ to a binary value so $x_i, y_i \to \{0, 1\}$.

    x_bin = Images.binarize(x_final, Images.Otsu(); nbins = 128)
 x_bin = convert(Array{Bool}, x_bin)
 plt = plot_dwt(img_roi)
-Plots.heatmap!(x_bin; color = :grays, alpha = 0.45)
    Example block output

    Edge detection and clustering

    Now that we have our binary image, we can use edge detection to find the edges of the galaxies. We will use the Sobel operator for this task.

    function edge_detector(
+Plots.heatmap!(x_bin; color = :grays, alpha = 0.45)
    Example block output

    Edge detection and clustering

    Now that we have our binary image, we can use edge detection to find the edges of the galaxies. We will use the Sobel operator for this task.

    function edge_detector(
     f_smooth::Matrix{Float64},
     d1::Float64 = 0.1,
     d2::Float64 = 0.1,
@@ -144,7 +144,7 @@
     legend = :topleft,
     legendcolumns = 1,
     legendfontsize = 12,
-)
    Example block output

    Fitting ellipses

    Now that we have all the ingredients we can finally start fitting ellipses. We will use a conic optimization approach to do so since it is a very natural way to represent ellipses.

    First, we define the residual distance definition (6) of a point to an ellipse in JuMP:

    function create_ellipse_model(Ξ::Array{Tuple{Int,Int},1}, ϵ = 1e-5)
+)
    Example block output

    Fitting ellipses

    Now that we have all the ingredients we can finally start fitting ellipses. We will use a conic optimization approach to do so since it is a very natural way to represent ellipses.

    First, we define the residual distance definition (6) of a point to an ellipse in JuMP:

    function create_ellipse_model(Ξ::Array{Tuple{Int,Int},1}, ϵ = 1e-5)
     N = length(Ξ)
     model = Model(Clarabel.Optimizer)
     set_silent(model)
@@ -204,7 +204,7 @@
         cbar = false,
     )
 end
-plt
    Example block output

    Objective 2: Minimize the maximum residual distance

    For our second objective we will minimize the maximum residual distance of all points to the ellipse:

    \[\min_{Q, d, e} \max_{\xi_i \in \mathcal{F}} d_\text{res}(\xi_i, \mathcal{E}) = +pltExample block output

    Objective 2: Minimize the maximum residual distance

    For our second objective we will minimize the maximum residual distance of all points to the ellipse:

    \[\min_{Q, d, e} \max_{\xi_i \in \mathcal{F}} d_\text{res}(\xi_i, \mathcal{E}) = \min_{Q, d, e} ||d_\text{res}||_\infty\]

    This objective can be implemented in JuMP using MOI.NormInfinityCone as follows:

    ellipses_C2 = Dict{Symbol,Any}[]
 for (i, cluster) in enumerate(clusters)
     p_cluster = points[:, cluster.core_indices]
@@ -237,4 +237,4 @@
     )
 end
 Plots.scatter!([0], [0]; color = :red, label = "Squared (Obj. 1)")
-Plots.scatter!([0], [0]; color = :green, label = "Min-Max (Obj. 2)")
    Example block output +Plots.scatter!([0], [0]; color = :green, label = "Min-Max (Obj. 2)")Example block output diff --git a/previews/PR3913/tutorials/conic/experiment_design/index.html b/previews/PR3913/tutorials/conic/experiment_design/index.html index dad337d8b70..f8cbd1c051e 100644 --- a/previews/PR3913/tutorials/conic/experiment_design/index.html +++ b/previews/PR3913/tutorials/conic/experiment_design/index.html @@ -99,4 +99,4 @@ 2.9157806299837166 2.67337566459234 2.735395012219622 - 0.3378388086258122 + 0.3378388086258122 diff --git a/previews/PR3913/tutorials/conic/introduction/index.html b/previews/PR3913/tutorials/conic/introduction/index.html index 885ce6371d8..ec919cc507d 100644 --- a/previews/PR3913/tutorials/conic/introduction/index.html +++ b/previews/PR3913/tutorials/conic/introduction/index.html @@ -6,4 +6,4 @@
    GitHub

    Introduction

    Conic programs are a class of convex nonlinear optimization problems which use cones to represent the nonlinearities. They have the form:

    \[\begin{align} & \min_{x \in \mathbb{R}^n} & f_0(x) \\ & \;\;\text{s.t.} & f_j(x) \in \mathcal{S}_j & \;\; j = 1 \ldots m -\end{align}\]

    Mixed-integer conic programs (MICPs) are extensions of conic programs in which some (or all) of the decision variables take discrete values.

    How to choose a solver

    JuMP supports a range of conic solvers, although support differs on what types of cones each solver supports. In the list of Supported solvers, "SOCP" denotes solvers supporting second-order cones and "SDP" denotes solvers supporting semidefinite cones. In addition, solvers such as SCS and Mosek have support for the exponential cone. Moreover, due to the bridging system in MathOptInterface, many of these solvers support a much wider range of exotic cones than they natively support. Solvers supporting discrete variables start with "(MI)" in the list of Supported solvers.

    Tip

    Duality plays a large role in solving conic optimization models. Depending on the solver, it can be more efficient to solve the dual instead of the primal. If performance is an issue, see the Dualization tutorial for more details.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    • The following tutorials are worked examples that present a problem in words, then formulate it in mathematics, and then solve it in JuMP. This usually involves some sort of visualization of the solution. Start here if you are new to JuMP.
    • The Modeling with cones tutorial contains a number of helpful reformulations and tricks you can use when modeling conic programs. Look here if you are stuck trying to formulate a problem as a conic program.
    • The remaining tutorials are less verbose and styled in the form of short code examples. These tutorials have less explanation, but may contain useful code snippets, particularly if they are similar to a problem you are trying to solve.
    +\end{align}\]

    Mixed-integer conic programs (MICPs) are extensions of conic programs in which some (or all) of the decision variables take discrete values.

    How to choose a solver

    JuMP supports a range of conic solvers, although support differs on what types of cones each solver supports. In the list of Supported solvers, "SOCP" denotes solvers supporting second-order cones and "SDP" denotes solvers supporting semidefinite cones. In addition, solvers such as SCS and Mosek have support for the exponential cone. Moreover, due to the bridging system in MathOptInterface, many of these solvers support a much wider range of exotic cones than they natively support. Solvers supporting discrete variables start with "(MI)" in the list of Supported solvers.

    Tip

    Duality plays a large role in solving conic optimization models. Depending on the solver, it can be more efficient to solve the dual instead of the primal. If performance is an issue, see the Dualization tutorial for more details.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    • The following tutorials are worked examples that present a problem in words, then formulate it in mathematics, and then solve it in JuMP. This usually involves some sort of visualization of the solution. Start here if you are new to JuMP.
    • The Modeling with cones tutorial contains a number of helpful reformulations and tricks you can use when modeling conic programs. Look here if you are stuck trying to formulate a problem as a conic program.
    • The remaining tutorials are less verbose and styled in the form of short code examples. These tutorials have less explanation, but may contain useful code snippets, particularly if they are similar to a problem you are trying to solve.
    diff --git a/previews/PR3913/tutorials/conic/logistic_regression/index.html b/previews/PR3913/tutorials/conic/logistic_regression/index.html index dd621edebc7..b71ec7b20d1 100644 --- a/previews/PR3913/tutorials/conic/logistic_regression/index.html +++ b/previews/PR3913/tutorials/conic/logistic_regression/index.html @@ -109,4 +109,4 @@ )
    Number of non-zero components: 8 (out of 10 features)

    Extensions

    A direct extension would be to consider the sparse logistic regression with hard thresholding, which, on contrary to the soft version using a $\ell_1$ regularization, adds an explicit cardinality constraint in its formulation:

    \[\begin{aligned} \min_{\theta} & \; \sum_{i=1}^n \log(1 + \exp(-y_i \theta^\top x_i)) + \lambda \| \theta \|_2^2 \\ \text{subject to } & \quad \| \theta \|_0 <= k -\end{aligned}\]

    where $k$ is the maximum number of non-zero components in the vector $\theta$, and $\|.\|_0$ is the $\ell_0$ pseudo-norm:

    \[\| x\|_0 = \#\{i : \; x_i \neq 0\}\]

    The cardinality constraint $\|\theta\|_0 \leq k$ could be reformulated with binary variables. Thus the hard sparse regression problem could be solved by any solver supporting mixed integer conic problems.

    +\end{aligned}\]

    where $k$ is the maximum number of non-zero components in the vector $\theta$, and $\|.\|_0$ is the $\ell_0$ pseudo-norm:

    \[\| x\|_0 = \#\{i : \; x_i \neq 0\}\]

    The cardinality constraint $\|\theta\|_0 \leq k$ could be reformulated with binary variables. Thus the hard sparse regression problem could be solved by any solver supporting mixed integer conic problems.

    diff --git a/previews/PR3913/tutorials/conic/min_ellipse/eb7e74c3.svg b/previews/PR3913/tutorials/conic/min_ellipse/06656430.svg similarity index 88% rename from previews/PR3913/tutorials/conic/min_ellipse/eb7e74c3.svg rename to previews/PR3913/tutorials/conic/min_ellipse/06656430.svg index 3373393d7f4..6e523065395 100644 --- a/previews/PR3913/tutorials/conic/min_ellipse/eb7e74c3.svg +++ b/previews/PR3913/tutorials/conic/min_ellipse/06656430.svg @@ -1,50 +1,50 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/conic/min_ellipse/574a59c0.svg b/previews/PR3913/tutorials/conic/min_ellipse/586c4693.svg similarity index 88% rename from previews/PR3913/tutorials/conic/min_ellipse/574a59c0.svg rename to previews/PR3913/tutorials/conic/min_ellipse/586c4693.svg index 8d517686cea..402f833a029 100644 --- a/previews/PR3913/tutorials/conic/min_ellipse/574a59c0.svg +++ b/previews/PR3913/tutorials/conic/min_ellipse/586c4693.svg @@ -1,53 +1,53 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/conic/min_ellipse/index.html b/previews/PR3913/tutorials/conic/min_ellipse/index.html index 85add2d894e..ec238963e44 100644 --- a/previews/PR3913/tutorials/conic/min_ellipse/index.html +++ b/previews/PR3913/tutorials/conic/min_ellipse/index.html @@ -46,7 +46,7 @@ for ellipse in ellipses plot_ellipse(plot, ellipse) end -plotExample block output

    Build the model

    Now let's build the model, using the change-of-variables P² = $P^2$ and P_q = $P q$. We'll recover the true value of P and q after the solve.

    model = Model(SCS.Optimizer)
+plot
    Example block output

    Build the model

    Now let's build the model, using the change-of-variables P² = $P^2$ and P_q = $P q$. We'll recover the true value of P and q after the solve.

    model = Model(SCS.Optimizer)
 # We need to use a tighter tolerance for this example, otherwise the bounding
 # ellipse won't actually be bounding...
 set_attribute(model, "eps_rel", 1e-6)
@@ -85,7 +85,7 @@
   Dual objective value : -4.04364e+00
 
 * Work counters
-  Solve time (sec)   : 2.22113e-01
+  Solve time (sec)   : 2.17053e-01

    Results

    After solving the model to optimality we can recover the solution in terms of $P$ and $q$:

    P = sqrt(value.(P²))
 q = P \ value.(P_q)
    2-element Vector{Float64}:
  -0.3964217693227084
@@ -94,4 +94,4 @@
     [tuple(P \ [cos(θ) - q[1], sin(θ) - q[2]]...) for θ in 0:0.05:(2pi+0.05)];
     c = :crimson,
     label = nothing,
-)
    Example block output +)Example block output diff --git a/previews/PR3913/tutorials/conic/quantum_discrimination/index.html b/previews/PR3913/tutorials/conic/quantum_discrimination/index.html index 7a0c4b5b475..c3d36c69b15 100644 --- a/previews/PR3913/tutorials/conic/quantum_discrimination/index.html +++ b/previews/PR3913/tutorials/conic/quantum_discrimination/index.html @@ -44,7 +44,7 @@ Dual objective value : 8.64062e-01 * Work counters - Solve time (sec) : 4.40547e-04 + Solve time (sec) : 4.21569e-04

    The probability of guessing correctly is:

    objective_value(model)
    0.8640614507314219

    When N = 2, there is a known analytical solution of:

    0.5 + 0.25 * sum(LinearAlgebra.svdvals(ρ[1] - ρ[2]))
    0.8640627582954737

    proving that we found the optimal solution.

    Finally, the optimal POVM is:

    solution = [value.(e) for e in E]
    2-element Vector{Matrix{ComplexF64}}:
  [0.9495721399750024 + 0.0im 0.03442451603977098 + 0.21609731371190505im; 0.03442451603977098 - 0.21609731371190505im 0.05042785512985496 + 0.0im]
  [0.05042785517602001 + 0.0im -0.03442451605312517 - 0.21609731370614843im; -0.03442451605312517 + 0.21609731370614843im 0.9495721400119357 + 0.0im]
    Tip

    Duality plays a large role in solving conic optimization models. Depending on the solver, it can be more efficient to solve the dual of this problem instead of the primal. If performance is an issue, see the Dualization tutorial for more details.

    Alternative formulation

    The formulation above includes N Hermitian matrices and a set of linear equality constraints. We can simplify the problem by replacing $E_N$ with $E_N = I - \sum\limits_{i=1}^{N-1} E_i$. This results in:

    model = Model(SCS.Optimizer)
@@ -71,5 +71,5 @@
   Dual objective value : 8.64062e-01
 
 * Work counters
-  Solve time (sec)   : 4.05180e-04
-
    objective_value(model)
    0.8640596603179975
    + Solve time (sec) : 4.08485e-04 +
    objective_value(model)
    0.8640596603179975
    diff --git a/previews/PR3913/tutorials/conic/simple_examples/d6d86983.svg b/previews/PR3913/tutorials/conic/simple_examples/c7c00151.svg similarity index 79% rename from previews/PR3913/tutorials/conic/simple_examples/d6d86983.svg rename to previews/PR3913/tutorials/conic/simple_examples/c7c00151.svg index 5658ba5afa7..7725bc09609 100644 --- a/previews/PR3913/tutorials/conic/simple_examples/d6d86983.svg +++ b/previews/PR3913/tutorials/conic/simple_examples/c7c00151.svg @@ -1,49 +1,49 @@ - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/conic/simple_examples/index.html b/previews/PR3913/tutorials/conic/simple_examples/index.html index b9764f65ac1..32a3def118f 100644 --- a/previews/PR3913/tutorials/conic/simple_examples/index.html +++ b/previews/PR3913/tutorials/conic/simple_examples/index.html @@ -196,7 +196,7 @@ ) end -example_minimum_distortion()Example block output

    Lovász numbers

    The Lovász number of a graph, also known as Lovász's theta-function, is a number that lies between two important and related numbers that are computationally hard to determine, namely the chromatic and clique numbers of the graph. It is possible however to efficient compute the Lovász number as the optimal value of a semidefinite program.

    Consider the pentagon graph:

         [5]
+example_minimum_distortion()
    Example block output

    Lovász numbers

    The Lovász number of a graph, also known as Lovász's theta-function, is a number that lies between two important and related numbers that are computationally hard to determine, namely the chromatic and clique numbers of the graph. It is possible however to efficient compute the Lovász number as the optimal value of a semidefinite program.

    Consider the pentagon graph:

         [5]
     /   \
    /     \
  [1]     [4]
@@ -259,4 +259,4 @@
     return
 end
 
-example_robust_uncertainty_sets()
    +example_robust_uncertainty_sets() diff --git a/previews/PR3913/tutorials/conic/start_values/index.html b/previews/PR3913/tutorials/conic/start_values/index.html index 00b3ce977ba..9af04abd407 100644 --- a/previews/PR3913/tutorials/conic/start_values/index.html +++ b/previews/PR3913/tutorials/conic/start_values/index.html @@ -52,12 +52,12 @@ ------------------------------------------------------------------ iter | pri res | dua res | gap | obj | scale | time (s) ------------------------------------------------------------------ - 0| 4.42e+01 1.00e+00 1.28e+02 -6.64e+01 1.00e-01 8.01e-05 - 75| 5.30e-07 2.63e-06 3.15e-07 -3.00e+00 1.00e-01 1.28e-04 + 0| 4.42e+01 1.00e+00 1.28e+02 -6.64e+01 1.00e-01 1.01e-04 + 75| 5.30e-07 2.63e-06 3.15e-07 -3.00e+00 1.00e-01 1.48e-04 ------------------------------------------------------------------ status: solved -timings: total: 1.29e-04s = setup: 3.87e-05s + solve: 8.99e-05s - lin-sys: 1.40e-05s, cones: 6.73e-06s, accel: 3.62e-06s +timings: total: 1.49e-04s = setup: 3.63e-05s + solve: 1.13e-04s + lin-sys: 1.39e-05s, cones: 6.37e-06s, accel: 3.70e-06s ------------------------------------------------------------------ objective = -2.999998 ------------------------------------------------------------------

    By looking at the log, we can see that SCS took 75 iterations to find the optimal solution. Now we set the optimal solution as our starting point:

    set_optimal_start_values(model)

    and we re-optimize:

    optimize!(model)
    ------------------------------------------------------------------
@@ -76,11 +76,11 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.90e-05  1.56e-06  9.14e-05 -3.00e+00  1.00e-01  7.97e-05
+     0| 1.90e-05  1.56e-06  9.14e-05 -3.00e+00  1.00e-01  1.24e-04
 ------------------------------------------------------------------
 status:  solved
-timings: total: 8.06e-05s = setup: 3.70e-05s + solve: 4.37e-05s
-	 lin-sys: 7.71e-07s, cones: 1.25e-06s, accel: 3.00e-08s
+timings: total: 1.25e-04s = setup: 3.57e-05s + solve: 8.96e-05s
+	 lin-sys: 8.22e-07s, cones: 1.21e-06s, accel: 3.00e-08s
 ------------------------------------------------------------------
 objective = -3.000044
-------------------------------------------------------------------

    Now the optimization terminates after 0 iterations because our starting point is already optimal.

    Caveats

    Some solvers do not support setting some parts of the starting solution, for example, they may support only set_start_value for variables.

    If you encounter an UnsupportedSupported attribute error for MOI.VariablePrimalStart, MOI.ConstraintPrimalStart, or MOI.ConstraintDualStart, comment out the corresponding part of the set_optimal_start_values function.

    +------------------------------------------------------------------

    Now the optimization terminates after 0 iterations because our starting point is already optimal.

    Caveats

    Some solvers do not support setting some parts of the starting solution, for example, they may support only set_start_value for variables.

    If you encounter an UnsupportedSupported attribute error for MOI.VariablePrimalStart, MOI.ConstraintPrimalStart, or MOI.ConstraintDualStart, comment out the corresponding part of the set_optimal_start_values function.

    diff --git a/previews/PR3913/tutorials/conic/tips_and_tricks/index.html b/previews/PR3913/tutorials/conic/tips_and_tricks/index.html index a15b0128355..973d8276e86 100644 --- a/previews/PR3913/tutorials/conic/tips_and_tricks/index.html +++ b/previews/PR3913/tutorials/conic/tips_and_tricks/index.html @@ -190,4 +190,4 @@ @constraint(model, X .== [1 2 3; 4 5 6]) optimize!(model) @assert is_solved_and_feasible(model) -value(t), maximum(LinearAlgebra.svdvals(value.(X)))
    (9.506936927003698, 9.508031076396836)

    Other Cones and Functions

    For other cones supported by JuMP, check out the MathOptInterface Manual.

    +value(t), maximum(LinearAlgebra.svdvals(value.(X)))
    (9.506936927003698, 9.508031076396836)

    Other Cones and Functions

    For other cones supported by JuMP, check out the MathOptInterface Manual.

    diff --git a/previews/PR3913/tutorials/getting_started/debugging/index.html b/previews/PR3913/tutorials/getting_started/debugging/index.html index 516b7c8b31e..6bc98776b21 100644 --- a/previews/PR3913/tutorials/getting_started/debugging/index.html +++ b/previews/PR3913/tutorials/getting_started/debugging/index.html @@ -24,4 +24,4 @@ julia> @profview foo(); # run once to trigger compilation. Ignore the output. -julia> @profview foo()

    This will open a flamegraph. The x-axis of the graph is time, so that wider bars take more time. The bars are stacked so that the foo() call is on the bottom, and subsequent calls within foo are stacked on top.

    Reading a flamegraph can take some experience, but if you click on a bar it will print the line number to the REPL. Hunt around until you find the widest bar that points to a line of code that you have written, then ask yourself if it makes sense for this line to be the bottleneck.

    If a wide bar points to code inside JuMP or a related Julia package, please open an issue on GitHub or post on the community forum.

    If @time foo() takes longer than a few minutes to run, then either make the problem smaller by using a smaller dataset, or do the following.

    1. Comment out everything in the function, then, line by line (or block by block):
    2. Un-comment some code and re-run @time foo()
    3. If the time increases by a lot (from seconds or minutes to hours), look for $O(N^2)$ or worse scaling behavior. Is there a better way to write the code that you are trying to execute?
    4. If the time increases by more than expected, but it still takes seconds or minutes to execute, use ProfileView to look for obvious bottlenecks.
    +julia> @profview foo()

    This will open a flamegraph. The x-axis of the graph is time, so that wider bars take more time. The bars are stacked so that the foo() call is on the bottom, and subsequent calls within foo are stacked on top.

    Reading a flamegraph can take some experience, but if you click on a bar it will print the line number to the REPL. Hunt around until you find the widest bar that points to a line of code that you have written, then ask yourself if it makes sense for this line to be the bottleneck.

    If a wide bar points to code inside JuMP or a related Julia package, please open an issue on GitHub or post on the community forum.

    If @time foo() takes longer than a few minutes to run, then either make the problem smaller by using a smaller dataset, or do the following.

    1. Comment out everything in the function, then, line by line (or block by block):
    2. Un-comment some code and re-run @time foo()
    3. If the time increases by a lot (from seconds or minutes to hours), look for $O(N^2)$ or worse scaling behavior. Is there a better way to write the code that you are trying to execute?
    4. If the time increases by more than expected, but it still takes seconds or minutes to execute, use ProfileView to look for obvious bottlenecks.
    diff --git a/previews/PR3913/tutorials/getting_started/design_patterns_for_larger_models/index.html b/previews/PR3913/tutorials/getting_started/design_patterns_for_larger_models/index.html index 13feb08a3bc..c9411fcad78 100644 --- a/previews/PR3913/tutorials/getting_started/design_patterns_for_larger_models/index.html +++ b/previews/PR3913/tutorials/getting_started/design_patterns_for_larger_models/index.html @@ -520,4 +520,4 @@ ) @test x === nothing end -end
    Test.DefaultTestSet("KnapsackModel", Any[Test.DefaultTestSet("feasible_binary_knapsack", Any[], 5, false, false, true, 1.736972097019207e9, 1.736972097021123e9, false, "design_patterns_for_larger_models.md"), Test.DefaultTestSet("feasible_integer_knapsack", Any[], 5, false, false, true, 1.736972097021157e9, 1.736972097143477e9, false, "design_patterns_for_larger_models.md"), Test.DefaultTestSet("infeasible_binary_knapsack", Any[], 1, false, false, true, 1.736972097143518e9, 1.736972097145097e9, false, "design_patterns_for_larger_models.md")], 0, false, false, true, 1.736972097019173e9, 1.736972097145104e9, false, "design_patterns_for_larger_models.md")
    Tip

    Place these tests in a separate file test_knapsack_model.jl so that you can run the tests by adding include("test_knapsack_model.jl") to any file where needed.

    Next steps

    We've only briefly scratched the surface of ways to create and structure large JuMP models, so consider this tutorial a starting point, rather than a comprehensive list of all the possible ways to structure JuMP models. If you are embarking on a large project that uses JuMP, a good next step is to look at ways people have written large JuMP projects "in the wild."

    Here are some good examples (all co-incidentally related to energy):

    +end
    Test.DefaultTestSet("KnapsackModel", Any[Test.DefaultTestSet("feasible_binary_knapsack", Any[], 5, false, false, true, 1.736976783122211e9, 1.736976783124072e9, false, "design_patterns_for_larger_models.md"), Test.DefaultTestSet("feasible_integer_knapsack", Any[], 5, false, false, true, 1.736976783124098e9, 1.736976783243166e9, false, "design_patterns_for_larger_models.md"), Test.DefaultTestSet("infeasible_binary_knapsack", Any[], 1, false, false, true, 1.736976783243207e9, 1.736976783244595e9, false, "design_patterns_for_larger_models.md")], 0, false, false, true, 1.736976783122177e9, 1.736976783244603e9, false, "design_patterns_for_larger_models.md")
    Tip

    Place these tests in a separate file test_knapsack_model.jl so that you can run the tests by adding include("test_knapsack_model.jl") to any file where needed.

    Next steps

    We've only briefly scratched the surface of ways to create and structure large JuMP models, so consider this tutorial a starting point, rather than a comprehensive list of all the possible ways to structure JuMP models. If you are embarking on a large project that uses JuMP, a good next step is to look at ways people have written large JuMP projects "in the wild."

    Here are some good examples (all co-incidentally related to energy):

    diff --git a/previews/PR3913/tutorials/getting_started/getting_started_with_JuMP/index.html b/previews/PR3913/tutorials/getting_started/getting_started_with_JuMP/index.html index 9cd4b05a832..f52e2fd73e9 100644 --- a/previews/PR3913/tutorials/getting_started/getting_started_with_JuMP/index.html +++ b/previews/PR3913/tutorials/getting_started/getting_started_with_JuMP/index.html @@ -242,4 +242,4 @@ Model status : Optimal Simplex iterations: 4 Objective value : 4.9230769231e+00 -HiGHS run time : 0.00
    julia> @assert is_solved_and_feasible(vector_model)
    julia> objective_value(vector_model)4.923076923076922 +HiGHS run time : 0.00
    julia> @assert is_solved_and_feasible(vector_model)
    julia> objective_value(vector_model)4.923076923076922 diff --git a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/15d638fa.svg b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/25f00548.svg similarity index 82% rename from previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/15d638fa.svg rename to previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/25f00548.svg index 68af68a1d6d..6fb6819159d 100644 --- a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/15d638fa.svg +++ b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/25f00548.svg @@ -1,73 +1,73 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/981f72b9.svg b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/27fdea48.svg similarity index 85% rename from previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/981f72b9.svg rename to previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/27fdea48.svg index c974f75062c..47cdf8e56d1 100644 --- a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/981f72b9.svg +++ b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/27fdea48.svg @@ -1,59 +1,59 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/8301dab4.svg b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/6111ee70.svg similarity index 84% rename from previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/8301dab4.svg rename to previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/6111ee70.svg index c82056eb93c..267054db733 100644 --- a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/8301dab4.svg +++ b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/6111ee70.svg @@ -1,62 +1,62 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/index.html b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/index.html index 190892ae2d3..c84a2263210 100644 --- a/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/index.html +++ b/previews/PR3913/tutorials/getting_started/getting_started_with_data_and_plotting/index.html @@ -14,7 +14,7 @@ csv_df.Height; xlabel = "Weight", ylabel = "Height", -)Example block output

    That doesn't look right. What happened? If you look at the dataframe above, it read Weight in as a String column because there are "NA" fields. Let's correct that, by telling CSV to consider "NA" as missing.

    csv_df = CSV.read(
+)
    Example block output

    That doesn't look right. What happened? If you look at the dataframe above, it read Weight in as a String column because there are "NA" fields. Let's correct that, by telling CSV to consider "NA" as missing.

    csv_df = CSV.read(
     joinpath(DATA_DIR, "StarWars.csv"),
     DataFrames.DataFrame;
     missingstring = "NA",
@@ -26,7 +26,7 @@
     ylabel = "Height",
     label = false,
     ylims = (0, 3),
-)
    Example block output

    That looks better.

    Tip

    Read the CSV documentation for other parsing options.

    DataFrames.jl supports manipulation using functions similar to pandas. For example, split the dataframe into groups based on eye-color:

    by_eyecolor = DataFrames.groupby(csv_df, :Eyecolor)

    GroupedDataFrame with 7 groups based on key: Eyecolor

    First Group (5 rows): Eyecolor = "blue"
    RowNameGenderHeightWeightEyecolorHaircolorSkincolorHomelandBornDiedJediSpeciesWeapon
    String31String7Float64Float64?String15?String7?String15?String15String15String15String7String15String15
    1Anakin Skywalkermale1.8884.0blueblondfairTatooine41.9BBY4ABYjedihumanlightsaber
    2Luke Skywalkermale1.7277.0blueblondfairTatooine19BBYunk_diedjedihumanlightsaber
    3Qui-Gon Jinnmale1.9388.5bluebrownlightunk_planet92BBY32BBYjedihumanlightsaber
    4Sheev Palpatinemale1.7375.0blueredpaleNaboo82BBY10ABYno_jedihumanforce-lightning
    5Chewbaccamale2.28112.0bluebrownmissingKashyyyk200BBY25ABYno_jediwookieebowcaster

    ⋮

    Last Group (1 row): Eyecolor = "black"
    RowNameGenderHeightWeightEyecolorHaircolorSkincolorHomelandBornDiedJediSpeciesWeapon
    String31String7Float64Float64?String15?String7?String15?String15String15String15String7String15String15
    1Chief Chirpamale1.050.0blackgraybrownEndorunk_born4ABYno_jediewokspear

    Then recombine into a single dataframe based on a function operating over the split dataframes:

    eyecolor_count = DataFrames.combine(by_eyecolor) do df
+)
    Example block output

    That looks better.

    Tip

    Read the CSV documentation for other parsing options.

    DataFrames.jl supports manipulation using functions similar to pandas. For example, split the dataframe into groups based on eye-color:

    by_eyecolor = DataFrames.groupby(csv_df, :Eyecolor)

    GroupedDataFrame with 7 groups based on key: Eyecolor

    First Group (5 rows): Eyecolor = "blue"
    RowNameGenderHeightWeightEyecolorHaircolorSkincolorHomelandBornDiedJediSpeciesWeapon
    String31String7Float64Float64?String15?String7?String15?String15String15String15String7String15String15
    1Anakin Skywalkermale1.8884.0blueblondfairTatooine41.9BBY4ABYjedihumanlightsaber
    2Luke Skywalkermale1.7277.0blueblondfairTatooine19BBYunk_diedjedihumanlightsaber
    3Qui-Gon Jinnmale1.9388.5bluebrownlightunk_planet92BBY32BBYjedihumanlightsaber
    4Sheev Palpatinemale1.7375.0blueredpaleNaboo82BBY10ABYno_jedihumanforce-lightning
    5Chewbaccamale2.28112.0bluebrownmissingKashyyyk200BBY25ABYno_jediwookieebowcaster

    ⋮

    Last Group (1 row): Eyecolor = "black"
    RowNameGenderHeightWeightEyecolorHaircolorSkincolorHomelandBornDiedJediSpeciesWeapon
    String31String7Float64Float64?String15?String7?String15?String15String15String15String7String15String15
    1Chief Chirpamale1.050.0blackgraybrownEndorunk_born4ABYno_jediewokspear

    Then recombine into a single dataframe based on a function operating over the split dataframes:

    eyecolor_count = DataFrames.combine(by_eyecolor) do df
     return DataFrames.nrow(df)
 end
    7×2 DataFrame
    RowEyecolorx1
    String15?Int64
    1blue5
    2brown8
    3bluegray1
    4missing2
    5yellow2
    6gold1
    7black1

    We can rename columns:

    DataFrames.rename!(eyecolor_count, :x1 => :count)
    7×2 DataFrame
    RowEyecolorcount
    String15?Int64
    1blue5
    2brown8
    3bluegray1
    4missing2
    5yellow2
    6gold1
    7black1

    Drop some missing rows:

    DataFrames.dropmissing!(eyecolor_count, :Eyecolor)
    6×2 DataFrame
    RowEyecolorcount
    String15Int64
    1blue5
    2brown8
    3bluegray1
    4yellow2
    5gold1
    6black1

    Then we can visualize the data:

    sort!(eyecolor_count, :count; rev = true)
 Plots.bar(
@@ -35,7 +35,7 @@
     xlabel = "Eye color",
     ylabel = "Number of characters",
     label = false,
-)
    Example block output

    Other Delimited Files

    We can also use the CSV.jl package to read any other delimited text file format.

    By default, CSV.File will try to detect a file's delimiter from the first 10 lines of the file.

    Candidate delimiters include ',', '\t', ' ', '|', ';', and ':'. If it can't auto-detect the delimiter, it will assume ','.

    Let's take the example of space separated data.

    ss_df = CSV.read(joinpath(DATA_DIR, "Cereal.txt"), DataFrames.DataFrame)
    23×10 DataFrame
    RowNameCupsCaloriesCarbsFatFiberPotassiumProteinSodiumSugars
    String31Float64Int64Float64Int64Float64Int64Int64Int64Int64
    1CapnCrunch0.7512012.020.035122012
    2CocoaPuffs1.011012.010.055118013
    3Trix1.011013.010.025114012
    4AppleJacks1.011011.001.030212514
    5CornChex1.011022.000.02522803
    6CornFlakes1.010021.001.03522902
    7Nut&Honey0.6712015.010.04021909
    8Smacks0.751109.011.04027015
    9MultiGrain1.010015.012.09022206
    10CracklinOat0.511010.034.016031407
    11GrapeNuts0.2511017.003.09031793
    12HoneyNutCheerios0.7511011.511.590325010
    13NutriGrain0.6714021.023.013032207
    14Product191.010020.001.04533203
    15TotalRaisinBran1.014015.014.0230319014
    16WheatChex0.6710017.013.011532303
    17Oatmeal0.513013.521.5120317010
    18Life0.6710012.022.09541506
    19Maypo1.010016.010.095403
    20QuakerOats0.510014.012.011041356
    21Muesli1.015016.033.0170415011
    22Cheerios1.2511017.022.010562901
    23SpecialK1.011016.001.05562303

    We can also specify the delimiter as follows:

    delim_df = CSV.read(
+)
    Example block output

    Other Delimited Files

    We can also use the CSV.jl package to read any other delimited text file format.

    By default, CSV.File will try to detect a file's delimiter from the first 10 lines of the file.

    Candidate delimiters include ',', '\t', ' ', '|', ';', and ':'. If it can't auto-detect the delimiter, it will assume ','.

    Let's take the example of space separated data.

    ss_df = CSV.read(joinpath(DATA_DIR, "Cereal.txt"), DataFrames.DataFrame)
    23×10 DataFrame
    RowNameCupsCaloriesCarbsFatFiberPotassiumProteinSodiumSugars
    String31Float64Int64Float64Int64Float64Int64Int64Int64Int64
    1CapnCrunch0.7512012.020.035122012
    2CocoaPuffs1.011012.010.055118013
    3Trix1.011013.010.025114012
    4AppleJacks1.011011.001.030212514
    5CornChex1.011022.000.02522803
    6CornFlakes1.010021.001.03522902
    7Nut&Honey0.6712015.010.04021909
    8Smacks0.751109.011.04027015
    9MultiGrain1.010015.012.09022206
    10CracklinOat0.511010.034.016031407
    11GrapeNuts0.2511017.003.09031793
    12HoneyNutCheerios0.7511011.511.590325010
    13NutriGrain0.6714021.023.013032207
    14Product191.010020.001.04533203
    15TotalRaisinBran1.014015.014.0230319014
    16WheatChex0.6710017.013.011532303
    17Oatmeal0.513013.521.5120317010
    18Life0.6710012.022.09541506
    19Maypo1.010016.010.095403
    20QuakerOats0.510014.012.011041356
    21Muesli1.015016.033.0170415011
    22Cheerios1.2511017.022.010562901
    23SpecialK1.011016.001.05562303

    We can also specify the delimiter as follows:

    delim_df = CSV.read(
     joinpath(DATA_DIR, "Soccer.txt"),
     DataFrames.DataFrame;
     delim = "::",
@@ -204,7 +204,7 @@
   Dual objective value : NaN
 
 * Work counters
-  Solve time (sec)   : 6.74891e-03
+  Solve time (sec)   : 6.43325e-03
   Simplex iterations : 26
   Barrier iterations : -1
   Node count         : 1
@@ -236,4 +236,4 @@
  * Uganda
  * United Arab Emirates
  * United States
- * Zimbabwe

    We need some passports, like New Zealand and the United States, which have widespread access to a large number of countries. However, we also need passports like North Korea which only have visa-free access to a very limited number of countries.

    Note

    We use value(x[c]) > 0.5 rather than value(x[c]) == 1 to avoid excluding solutions like x[c] = 0.99999 that are "1" to some tolerance.

    + * Zimbabwe

    We need some passports, like New Zealand and the United States, which have widespread access to a large number of countries. However, we also need passports like North Korea which only have visa-free access to a very limited number of countries.

    Note

    We use value(x[c]) > 0.5 rather than value(x[c]) == 1 to avoid excluding solutions like x[c] = 0.99999 that are "1" to some tolerance.

    diff --git a/previews/PR3913/tutorials/getting_started/getting_started_with_julia/index.html b/previews/PR3913/tutorials/getting_started/getting_started_with_julia/index.html index 3c582cbc6cc..9b3083937e8 100644 --- a/previews/PR3913/tutorials/getting_started/getting_started_with_julia/index.html +++ b/previews/PR3913/tutorials/getting_started/getting_started_with_julia/index.html @@ -43,9 +43,9 @@ *(::Any, ::Any, ::Any, ::Any...) @ Base operators.jl:596 *(::Type{<:LinearOperatorCollection.ProdOp}, ::Any, ::Any) - @ LinearOperatorCollection ~/.julia/packages/LinearOperatorCollection/GRBTA/src/ProdOp.jl:73 - *(::ChainRulesCore.NotImplemented, ::Any) - @ ChainRulesCore ~/.julia/packages/ChainRulesCore/U6wNx/src/tangent_arithmetic.jl:37 + @ LinearOperatorCollection ~/.julia/packages/LinearOperatorCollection/GRBTA/src/ProdOp.jl:73 + *(::Graphs.LinAlg.Noop, ::Any) + @ Graphs ~/.julia/packages/Graphs/1ALGD/src/linalg/graphmatrices.jl:216 ...

    But multiplying transposes works:

    julia> b' * b61
    julia> b * b'2×2 Matrix{Int64}:
  25  30
  30  36

    Other common types

    Comments

    Although not technically a type, code comments begin with the # character:

    julia> 1 + 1  # This is a comment2

    Multiline comments begin with #= and end with =#:

    #=
@@ -182,4 +182,4 @@
  0.5103924401614957
  0.9296414851080324

    The Package Manager is used to install packages that are not part of Julia's standard library.

    For example the following can be used to install JuMP,

    using Pkg
 Pkg.add("JuMP")

    For a complete list of registered Julia packages see the package listing at JuliaHub.

    From time to you may wish to use a Julia package that is not registered. In this case a git repository URL can be used to install the package.

    using Pkg
-Pkg.add("https://github.com/user-name/MyPackage.jl.git")

    Package environments

    By default, Pkg.add will add packages to Julia's global environment. However, Julia also has built-in support for virtual environments.

    Activate a virtual environment with:

    import Pkg; Pkg.activate("/path/to/environment")

    You can see what packages are installed in the current environment with Pkg.status().

    Tip

    We strongly recommend you create a Pkg environment for each project that you create in Julia, and add only the packages that you need, instead of adding lots of packages to the global environment. The Pkg manager documentation has more information on this topic.

    +Pkg.add("https://github.com/user-name/MyPackage.jl.git")

    Package environments

    By default, Pkg.add will add packages to Julia's global environment. However, Julia also has built-in support for virtual environments.

    Activate a virtual environment with:

    import Pkg; Pkg.activate("/path/to/environment")

    You can see what packages are installed in the current environment with Pkg.status().

    Tip

    We strongly recommend you create a Pkg environment for each project that you create in Julia, and add only the packages that you need, instead of adding lots of packages to the global environment. The Pkg manager documentation has more information on this topic.

    diff --git a/previews/PR3913/tutorials/getting_started/getting_started_with_sets_and_indexing/index.html b/previews/PR3913/tutorials/getting_started/getting_started_with_sets_and_indexing/index.html index 908f424409e..6d6fdf4b8d8 100644 --- a/previews/PR3913/tutorials/getting_started/getting_started_with_sets_and_indexing/index.html +++ b/previews/PR3913/tutorials/getting_started/getting_started_with_sets_and_indexing/index.html @@ -219,4 +219,4 @@ ("Dunedin", "Auckland") => 1426 ("Auckland", "Christchurch") => 1071

    Then, we can create our model like so:

    model = Model()
 @variable(model, x[keys(routes)])
-@objective(model, Min, sum(v * x[k] for (k, v) in routes))

    \[ 643 x_{("Auckland", "Wellington")} + 436 x_{("Wellington", "Christchurch")} + 790 x_{("Wellington", "Dunedin")} + 360 x_{("Christchurch", "Dunedin")} + 1426 x_{("Auckland", "Dunedin")} + 1426 x_{("Dunedin", "Auckland")} + 1071 x_{("Auckland", "Christchurch")} \]

    This has a number of benefits over the other approaches, including a compacter algebraic model and variables that are named in a more meaningful way.

    Tip

    If you're struggling to formulate a problem using the available syntax in JuMP, it's probably a sign that you should convert your data into a different form.

    Next steps

    The purpose of this tutorial was to show how JuMP does not have specialized syntax for set creation and manipulation. Instead, you should use the tools provided by Julia itself.

    This is both an opportunity and a challenge, because you are free to pick the syntax and data structures that best suit your problem, but for new users it can be daunting to decide which structure to use.

    Read through some of the other JuMP tutorials to get inspiration and ideas for how you can use Julia's syntax and data structures to your advantage.

    +@objective(model, Min, sum(v * x[k] for (k, v) in routes))

    \[ 643 x_{("Auckland", "Wellington")} + 436 x_{("Wellington", "Christchurch")} + 790 x_{("Wellington", "Dunedin")} + 360 x_{("Christchurch", "Dunedin")} + 1426 x_{("Auckland", "Dunedin")} + 1426 x_{("Dunedin", "Auckland")} + 1071 x_{("Auckland", "Christchurch")} \]

    This has a number of benefits over the other approaches, including a compacter algebraic model and variables that are named in a more meaningful way.

    Tip

    If you're struggling to formulate a problem using the available syntax in JuMP, it's probably a sign that you should convert your data into a different form.

    Next steps

    The purpose of this tutorial was to show how JuMP does not have specialized syntax for set creation and manipulation. Instead, you should use the tools provided by Julia itself.

    This is both an opportunity and a challenge, because you are free to pick the syntax and data structures that best suit your problem, but for new users it can be daunting to decide which structure to use.

    Read through some of the other JuMP tutorials to get inspiration and ideas for how you can use Julia's syntax and data structures to your advantage.

    diff --git a/previews/PR3913/tutorials/getting_started/introduction/index.html b/previews/PR3913/tutorials/getting_started/introduction/index.html index 7326e051b70..a7da02fb195 100644 --- a/previews/PR3913/tutorials/getting_started/introduction/index.html +++ b/previews/PR3913/tutorials/getting_started/introduction/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-0RZ8X3D3D0', {'page_path': location.pathname + location.search + location.hash}); -
    GitHub

    Introduction

    The purpose of these "Getting started" tutorials is to teach new users the basics of Julia and JuMP.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    • The "Getting started with" tutorials are basic introductions to different aspects of JuMP and Julia. If you are new to JuMP and Julia, start by reading them in the following order:
    • Julia has a reputation for being "fast." Unfortunately, it is also easy to write slow Julia code. Performance tips contains a number of important tips on how to improve the performance of models you write in JuMP.
    • Design patterns for larger models is a more advanced tutorial that is aimed at users writing large JuMP models. It's in the "Getting started" section to give you an early preview of how JuMP makes it easy to structure larger models. If you are new to JuMP you may want to skip or briefly skim this tutorial, and come back to it once you have written a few JuMP models.
    +
    GitHub

    Introduction

    The purpose of these "Getting started" tutorials is to teach new users the basics of Julia and JuMP.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    • The "Getting started with" tutorials are basic introductions to different aspects of JuMP and Julia. If you are new to JuMP and Julia, start by reading them in the following order:
    • Julia has a reputation for being "fast." Unfortunately, it is also easy to write slow Julia code. Performance tips contains a number of important tips on how to improve the performance of models you write in JuMP.
    • Design patterns for larger models is a more advanced tutorial that is aimed at users writing large JuMP models. It's in the "Getting started" section to give you an early preview of how JuMP makes it easy to structure larger models. If you are new to JuMP you may want to skip or briefly skim this tutorial, and come back to it once you have written a few JuMP models.
    diff --git a/previews/PR3913/tutorials/getting_started/performance_tips/index.html b/previews/PR3913/tutorials/getting_started/performance_tips/index.html index 5bd24db25bb..86832013847 100644 --- a/previews/PR3913/tutorials/getting_started/performance_tips/index.html +++ b/previews/PR3913/tutorials/getting_started/performance_tips/index.html @@ -37,4 +37,4 @@ └ Names registered in the model: none
    julia> @variable(model, x[1:3])3-element Vector{VariableRef}: x[1] x[2] - x[3]

    Here's what happens if we construct the expression outside the macro:

    julia> @allocated x[1] + x[2] + x[3]1296
    Info

    The @allocated measures how many bytes were allocated during the evaluation of an expression. Fewer is better.

    If we use the @expression macro, we get many fewer allocations:

    julia> @allocated @expression(model, x[1] + x[2] + x[3])640

    Disable string names

    By default, JuMP creates String names for variables and constraints and passes these to the solver. The benefit of passing names is that it improves the readability of log messages from the solver (for example, "variable x has invalid bounds" instead of "variable v1203 has invalid bounds"), but for larger models the overhead of passing names can be non-trivial.

    Disable the creation of String names by setting set_string_name = false in the @variable and @constraint macros, or by calling set_string_names_on_creation to disable all names for a particular model:

    julia> model = Model();
    julia> set_string_names_on_creation(model, false)
    julia> @variable(model, x)_[1]
    julia> @constraint(model, c, 2x <= 1)2 _[1] ≤ 1

    Note that this doesn't change how symbolic names and bindings are stored:

    julia> x_[1]
    julia> model[:x]_[1]
    julia> x === model[:x]true

    But you can no longer look up the variable by the string name:

    julia> variable_by_name(model, "x") === nothingtrue
    Info

    For more information on the difference between string names, symbolic names, and bindings, see String names, symbolic names, and bindings.

    + x[3]

    Here's what happens if we construct the expression outside the macro:

    julia> @allocated x[1] + x[2] + x[3]1296
    Info

    The @allocated measures how many bytes were allocated during the evaluation of an expression. Fewer is better.

    If we use the @expression macro, we get many fewer allocations:

    julia> @allocated @expression(model, x[1] + x[2] + x[3])640

    Disable string names

    By default, JuMP creates String names for variables and constraints and passes these to the solver. The benefit of passing names is that it improves the readability of log messages from the solver (for example, "variable x has invalid bounds" instead of "variable v1203 has invalid bounds"), but for larger models the overhead of passing names can be non-trivial.

    Disable the creation of String names by setting set_string_name = false in the @variable and @constraint macros, or by calling set_string_names_on_creation to disable all names for a particular model:

    julia> model = Model();
    julia> set_string_names_on_creation(model, false)
    julia> @variable(model, x)_[1]
    julia> @constraint(model, c, 2x <= 1)2 _[1] ≤ 1

    Note that this doesn't change how symbolic names and bindings are stored:

    julia> x_[1]
    julia> model[:x]_[1]
    julia> x === model[:x]true

    But you can no longer look up the variable by the string name:

    julia> variable_by_name(model, "x") === nothingtrue
    Info

    For more information on the difference between string names, symbolic names, and bindings, see String names, symbolic names, and bindings.

    diff --git a/previews/PR3913/tutorials/getting_started/sum_if/8c11c9f5.svg b/previews/PR3913/tutorials/getting_started/sum_if/242b0d1c.svg similarity index 60% rename from previews/PR3913/tutorials/getting_started/sum_if/8c11c9f5.svg rename to previews/PR3913/tutorials/getting_started/sum_if/242b0d1c.svg index 3e61e2ada88..b669f03900f 100644 --- a/previews/PR3913/tutorials/getting_started/sum_if/8c11c9f5.svg +++ b/previews/PR3913/tutorials/getting_started/sum_if/242b0d1c.svg @@ -1,68 +1,68 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/getting_started/sum_if/624e5e6f.svg b/previews/PR3913/tutorials/getting_started/sum_if/93bd60b7.svg similarity index 55% rename from previews/PR3913/tutorials/getting_started/sum_if/624e5e6f.svg rename to previews/PR3913/tutorials/getting_started/sum_if/93bd60b7.svg index 47f5d7e1d0b..3560ba7b629 100644 --- a/previews/PR3913/tutorials/getting_started/sum_if/624e5e6f.svg +++ b/previews/PR3913/tutorials/getting_started/sum_if/93bd60b7.svg @@ -1,55 +1,55 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/getting_started/sum_if/index.html b/previews/PR3913/tutorials/getting_started/sum_if/index.html index eba3af7c11a..14c63c83521 100644 --- a/previews/PR3913/tutorials/getting_started/sum_if/index.html +++ b/previews/PR3913/tutorials/getting_started/sum_if/index.html @@ -64,7 +64,7 @@ end nodes, edges, demand = build_random_graph(1_000, 2_000) -@elapsed build_naive_model(nodes, edges, demand)
    0.116239978

    A good way to benchmark is to measure the runtime across a wide range of input sizes. From our big-O analysis, we should expect that doubling the number of nodes and edges results in a 4x increase in the runtime.

    run_times = Float64[]
+@elapsed build_naive_model(nodes, edges, demand)
    0.200020119

    A good way to benchmark is to measure the runtime across a wide range of input sizes. From our big-O analysis, we should expect that doubling the number of nodes and edges results in a 4x increase in the runtime.

    run_times = Float64[]
 factors = 1:10
 for factor in factors
     graph = build_random_graph(1_000 * factor, 5_000 * factor)
@@ -73,7 +73,7 @@
 Plots.plot(; xlabel = "Factor", ylabel = "Runtime [s]")
 Plots.scatter!(factors, run_times; label = "Actual")
 a, b = hcat(ones(10), factors .^ 2) \ run_times
-Plots.plot!(factors, a .+ b * factors .^ 2; label = "Quadratic fit")
    Example block output

    As expected, the runtimes demonstrate quadratic scaling: if we double the number of nodes and edges, the runtime increases by a factor of four.

    Caching

    We can improve our formulation by caching the list of incoming and outgoing nodes for each node n:

    out_nodes = Dict(n => Int[] for n in nodes)
+Plots.plot!(factors, a .+ b * factors .^ 2; label = "Quadratic fit")
    Example block output

    As expected, the runtimes demonstrate quadratic scaling: if we double the number of nodes and edges, the runtime increases by a factor of four.

    Caching

    We can improve our formulation by caching the list of incoming and outgoing nodes for each node n:

    out_nodes = Dict(n => Int[] for n in nodes)
 in_nodes = Dict(n => Int[] for n in nodes)
 for (i, j) in edges
     push!(out_nodes[i], j)
@@ -104,7 +104,7 @@
 end
 
 nodes, edges, demand = build_random_graph(1_000, 2_000)
-@elapsed build_cached_model(nodes, edges, demand)
    0.160647914

    Analysis

    Now we can analyse the difference in runtime of the two formulations:

    run_times_naive = Float64[]
+@elapsed build_cached_model(nodes, edges, demand)
    0.158455476

    Analysis

    Now we can analyse the difference in runtime of the two formulations:

    run_times_naive = Float64[]
 run_times_cached = Float64[]
 factors = 1:10
 for factor in factors
@@ -118,4 +118,4 @@
 Plots.plot!(factors, a .+ b * factors .^ 2; label = "Quadratic fit")
 Plots.scatter!(factors, run_times_cached; label = "Cached")
 a, b = hcat(ones(10), factors) \ run_times_cached
-Plots.plot!(factors, a .+ b * factors; label = "Linear fit")
    Example block output

    Even though the cached model needs to build in_nodes and out_nodes, it is asymptotically faster than the naïve model, scaling linearly with factor rather than quadratically.

    Lesson

    If you write code with sum-if type conditions, for example, @constraint(model, [a in set], sum(x[b] for b in list if condition(a, b)), you can improve the performance by caching the elements for which condition(a, b) is true.

    Finally, you should understand that this behavior is not specific to JuMP, and that it applies more generally to all computer programs you might write. (Python programs that use Pyomo or gurobipy would similarly benefit from this caching approach.)

    Understanding big-O notation and algorithmic complexity is a useful debugging skill to have, regardless of the type of program that you are writing.

    +Plots.plot!(factors, a .+ b * factors; label = "Linear fit")Example block output

    Even though the cached model needs to build in_nodes and out_nodes, it is asymptotically faster than the naïve model, scaling linearly with factor rather than quadratically.

    Lesson

    If you write code with sum-if type conditions, for example, @constraint(model, [a in set], sum(x[b] for b in list if condition(a, b)), you can improve the performance by caching the elements for which condition(a, b) is true.

    Finally, you should understand that this behavior is not specific to JuMP, and that it applies more generally to all computer programs you might write. (Python programs that use Pyomo or gurobipy would similarly benefit from this caching approach.)

    Understanding big-O notation and algorithmic complexity is a useful debugging skill to have, regardless of the type of program that you are writing.

    diff --git a/previews/PR3913/tutorials/getting_started/tolerances/index.html b/previews/PR3913/tutorials/getting_started/tolerances/index.html index 64ac10d5293..7cea95d732c 100644 --- a/previews/PR3913/tutorials/getting_started/tolerances/index.html +++ b/previews/PR3913/tutorials/getting_started/tolerances/index.html @@ -37,34 +37,34 @@ ------------------------------------------------------------------ iter | pri res | dua res | gap | obj | scale | time (s) ------------------------------------------------------------------ - 0| 2.00e+01 1.00e+00 2.00e+01 -9.98e+00 1.00e-01 3.41e-02 - 100| 6.92e-05 7.92e-05 7.33e-06 2.41e-05 1.00e-01 9.26e-02 + 0| 2.00e+01 1.00e+00 2.00e+01 -9.98e+00 1.00e-01 3.46e-02 + 100| 6.92e-05 7.92e-05 7.33e-06 2.41e-05 1.00e-01 9.27e-02 ------------------------------------------------------------------ status: solved -timings: total: 9.26e-02s = setup: 3.30e-02s + solve: 5.96e-02s - lin-sys: 5.05e-02s, cones: 2.12e-03s, accel: 7.24e-04s +timings: total: 9.27e-02s = setup: 3.35e-02s + solve: 5.92e-02s + lin-sys: 5.03e-02s, cones: 2.15e-03s, accel: 6.91e-04s ------------------------------------------------------------------ objective = 0.000024 ------------------------------------------------------------------

    SCS reports that it solved the problem to optimality:

    is_solved_and_feasible(model)
    true

    and that the solution for x[1] is nearly zero:

    value(x[1])
    2.04406873858532e-5

    However, the analytic solution for x[1] is:

    1 - n * ε / 2
    0.8479

    The answer is very wrong, and there is no indication from the solver that anything untoward happened. What's going on?

    One useful debugging tool is primal_feasibility_report:

    report = primal_feasibility_report(model)
    Dict{Any, Float64} with 8192 entries:
-  x[5374] ≥ 0 => 2.17278e-5
-  x[991] ≥ 0  => 2.01984e-5
-  x[2399] ≥ 0 => 1.8669e-5
-  x[2829] ≥ 0 => 1.56101e-5
-  x[5488] ≥ 0 => 2.17278e-5
-  x[3677] ≥ 0 => 1.8669e-5
-  x[945] ≥ 0  => 1.56101e-5
-  x[6806] ≥ 0 => 1.8669e-5
-  x[7322] ≥ 0 => 1.8669e-5
-  x[4716] ≥ 0 => 1.8669e-5
-  x[3181] ≥ 0 => 1.71395e-5
-  x[149] ≥ 0  => 1.25513e-5
-  x[570] ≥ 0  => 1.56101e-5
-  x[3160] ≥ 0 => 1.8669e-5
-  x[6903] ≥ 0 => 2.17278e-5
-  x[6481] ≥ 0 => 1.56101e-5
-  x[5462] ≥ 0 => 1.8669e-5
-  x[6053] ≥ 0 => 1.8669e-5
-  x[943] ≥ 0  => 1.8669e-5
+  x[1247] ≥ 0 => 1.8669e-5
+  x[7072] ≥ 0 => 2.32572e-5
+  x[7216] ≥ 0 => 2.01984e-5
+  x[3118] ≥ 0 => 1.71395e-5
+  x[7925] ≥ 0 => 2.17278e-5
+  x[3545] ≥ 0 => 1.8669e-5
+  x[1582] ≥ 0 => 1.71395e-5
+  x[7839] ≥ 0 => 2.17278e-5
+  x[3581] ≥ 0 => 2.17278e-5
+  x[234] ≥ 0  => 1.56101e-5
+  x[2983] ≥ 0 => 1.8669e-5
+  x[4448] ≥ 0 => 2.01984e-5
+  x[4729] ≥ 0 => 1.71395e-5
+  x[5324] ≥ 0 => 1.8669e-5
+  x[5539] ≥ 0 => 1.71395e-5
+  x[6189] ≥ 0 => 1.56101e-5
+  x[5859] ≥ 0 => 1.8669e-5
+  x[5960] ≥ 0 => 2.01984e-5
+  x[2514] ≥ 0 => 1.71395e-5
   ⋮           => ⋮

    report is a dictionary which maps constraints to the violation. The largest violation is approximately 1e-5:

    maximum(values(report))
    6.92133754155444e-5

    This makes sense, because the default primal feasibility tolerance for SCS is 1e-4.

    Most of the entries are lower bound constraints on the variables. Here are all the variables which violate their lower bound:

    violated_variables = filter(xi -> value(xi) < 0, x)
    8178-element Vector{VariableRef}:
  x[4]
  x[6]
@@ -105,13 +105,13 @@
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
      0| 2.00e+01  1.00e+00  2.00e+01 -9.98e+00  1.00e-01  3.44e-02
-   250| 2.01e-02  2.85e-04  2.00e-02  3.01e-02  3.86e-01  1.84e-01
-   500| 3.69e-04  5.93e-04  8.84e-05  8.48e-01  6.13e-01  3.36e-01
-   550| 2.66e-06  6.58e-10  1.27e-05  8.48e-01  6.13e-01  3.66e-01
+   250| 2.01e-02  2.85e-04  2.00e-02  3.01e-02  3.86e-01  1.85e-01
+   500| 3.69e-04  5.93e-04  8.84e-05  8.48e-01  6.13e-01  3.37e-01
+   550| 2.66e-06  6.58e-10  1.27e-05  8.48e-01  6.13e-01  3.67e-01
 ------------------------------------------------------------------
 status:  solved
-timings: total: 3.66e-01s = setup: 3.34e-02s + solve: 3.33e-01s
-	 lin-sys: 2.74e-01s, cones: 1.16e-02s, accel: 5.71e-03s
+timings: total: 3.67e-01s = setup: 3.33e-02s + solve: 3.34e-01s
+	 lin-sys: 2.74e-01s, cones: 1.15e-02s, accel: 5.70e-03s
 ------------------------------------------------------------------
 objective = 0.847906
 ------------------------------------------------------------------
    @assert is_solved_and_feasible(model)
@@ -159,11 +159,11 @@
 @variable(model, x >= 0)
 @variable(model, y, Bin)
 @constraint(model, 1e-6x <= 1e6 * y)

    \[ 1.0 \times 10^{-6} x - 1000000 y \leq 0 \]

    This problem has a feasible (to tolerance) solution of:

    primal_feasibility_report(model, Dict(x => 1_000_000.01, y => 1e-6))
    Dict{Any, Float64} with 2 entries:
-  1.0e-6 x - 1000000 y ≤ 0 => 1.0e-8
-  y binary                 => 1.0e-6

    If you intended the constraint to read that if x is non-zero then y = 1, this solution might be unexpected.

    There are no hard rules that you must follow, and the interaction between tolerances, problem scaling, and the solution is problem dependent. You should always check the solution returned by the solver to check it makes sense for your application.

    With that caveat in mind, a general rule of thumb to follow is:

    Try to keep the ratio of the smallest to largest coefficient less than $10^6$ in any row and column, and try to keep most values between $10^{-3}$ and $10^6$.

    Choosing the correct units

    The best way to fix problem scaling is by changing the units of your variables and constraints. Here's an example. Suppose we are choosing the level of capacity investment in a new power plant. We can install up to 1 GW of capacity at a cost of $1.78/W, and we have a budget of $200 million.

    model = Model()
+  y binary                 => 1.0e-6
+  1.0e-6 x - 1000000 y ≤ 0 => 1.0e-8

    If you intended the constraint to read that if x is non-zero then y = 1, this solution might be unexpected.

    There are no hard rules that you must follow, and the interaction between tolerances, problem scaling, and the solution is problem dependent. You should always check the solution returned by the solver to check it makes sense for your application.

    With that caveat in mind, a general rule of thumb to follow is:

    Try to keep the ratio of the smallest to largest coefficient less than $10^6$ in any row and column, and try to keep most values between $10^{-3}$ and $10^6$.

    Choosing the correct units

    The best way to fix problem scaling is by changing the units of your variables and constraints. Here's an example. Suppose we are choosing the level of capacity investment in a new power plant. We can install up to 1 GW of capacity at a cost of $1.78/W, and we have a budget of $200 million.

    model = Model()
 @variable(model, 0 <= x_capacity_W <= 10^9)
 @constraint(model, 1.78 * x_capacity_W <= 200e6)

    \[ 1.78 x\_capacity\_W \leq 200000000 \]

    This constraint violates the recommendations because there are values greater than $10^6$, and the ratio of the coefficients in the constraint is $10^8$.

    One fix is the convert our capacity variable from Watts to Megawatts. This yields:

    model = Model()
 @variable(model, 0 <= x_capacity_MW <= 10^3)
 @constraint(model, 1.78e6 * x_capacity_MW <= 200e6)

    \[ 1780000 x\_capacity\_MW \leq 200000000 \]

    We can improve our model further by dividing the constraint by $10^6$ to change the units from dollars to million dollars.

    model = Model()
 @variable(model, 0 <= x_capacity_MW <= 10^3)
-@constraint(model, 1.78 * x_capacity_MW <= 200)

    \[ 1.78 x\_capacity\_MW \leq 200 \]

    This problem is equivalent to the original problem, but it has much better problem scaling.

    As a general rule, to fix problem scaling you must simultaneously scale both variables and constraints. It is usually not sufficient to scale variables or constraints in isolation.

    +@constraint(model, 1.78 * x_capacity_MW <= 200)

    \[ 1.78 x\_capacity\_MW \leq 200 \]

    This problem is equivalent to the original problem, but it has much better problem scaling.

    As a general rule, to fix problem scaling you must simultaneously scale both variables and constraints. It is usually not sufficient to scale variables or constraints in isolation.

    diff --git a/previews/PR3913/tutorials/linear/basis/index.html b/previews/PR3913/tutorials/linear/basis/index.html index 07d1708e5ba..e0f253b7f50 100644 --- a/previews/PR3913/tutorials/linear/basis/index.html +++ b/previews/PR3913/tutorials/linear/basis/index.html @@ -60,9 +60,9 @@ ci => get_attribute(ci, MOI.ConstraintBasisStatus()) for ci in all_constraints(model; include_variable_in_set_constraints = false) )
    Dict{ConstraintRef{Model, C, ScalarShape} where C, MathOptInterface.BasisStatusCode} with 3 entries:
-  c2 : 7 x + 12 y ≥ 120 => NONBASIC
+  c3 : x + y ≤ 20       => BASIC
   c1 : 6 x + 8 y ≥ 100  => NONBASIC
-  c3 : x + y ≤ 20       => BASIC

    Thus, the basis is formed by x, y, and the slack associated with c3.

    A simple way to get the A matrix of an unstructured linear program is with lp_matrix_data:

    matrix = lp_matrix_data(model)
+  c2 : 7 x + 12 y ≥ 120 => NONBASIC

    Thus, the basis is formed by x, y, and the slack associated with c3.

    A simple way to get the A matrix of an unstructured linear program is with lp_matrix_data:

    matrix = lp_matrix_data(model)
 matrix.A
    3×3 SparseArrays.SparseMatrixCSC{Float64, Int64} with 6 stored entries:
  6.0   8.0   ⋅ 
  7.0  12.0   ⋅ 
@@ -96,4 +96,4 @@
 @constraint(model, A * x == b)
 optimize!(model)
 degenerate_variables = filter(is_degenerate, all_variables(model))
    1-element Vector{VariableRef}:
- x[1]

    The solution is degenerate because:

    value(x[1])
    -0.0

    and

    get_attribute(x[1], MOI.VariableBasisStatus())
    BASIC::BasisStatusCode = 0
    + x[1]

    The solution is degenerate because:

    value(x[1])
    -0.0

    and

    get_attribute(x[1], MOI.VariableBasisStatus())
    BASIC::BasisStatusCode = 0
    diff --git a/previews/PR3913/tutorials/linear/callbacks/index.html b/previews/PR3913/tutorials/linear/callbacks/index.html index 250652b8ff4..1c0882560d2 100644 --- a/previews/PR3913/tutorials/linear/callbacks/index.html +++ b/previews/PR3913/tutorials/linear/callbacks/index.html @@ -246,4 +246,4 @@ Solve interrupted Best objective -, best bound -, gap - -User-callback calls 31, time in user-callback 0.03 sec +User-callback calls 31, time in user-callback 0.03 sec diff --git a/previews/PR3913/tutorials/linear/cannery/index.html b/previews/PR3913/tutorials/linear/cannery/index.html index fca3f5ddf93..aaf0a4695bc 100644 --- a/previews/PR3913/tutorials/linear/cannery/index.html +++ b/previews/PR3913/tutorials/linear/cannery/index.html @@ -76,7 +76,7 @@ Dual objective value : 1.68000e+03 * Work counters - Solve time (sec) : 2.33412e-04 + Solve time (sec) : 1.88112e-04 Simplex iterations : 3 Barrier iterations : 0 Node count : -1 @@ -88,4 +88,4 @@ Seattle => New-York: 0.0 San-Diego => Chicago: 0.0 San-Diego => Topeka: 300.0 -San-Diego => New-York: 300.0 +San-Diego => New-York: 300.0 diff --git a/previews/PR3913/tutorials/linear/constraint_programming/index.html b/previews/PR3913/tutorials/linear/constraint_programming/index.html index b6aff249d61..a53bf3ddaa9 100644 --- a/previews/PR3913/tutorials/linear/constraint_programming/index.html +++ b/previews/PR3913/tutorials/linear/constraint_programming/index.html @@ -97,4 +97,4 @@ value.(x)
    3-element Vector{Float64}:
  1.0
  1.0
- 0.0
    + 0.0 diff --git a/previews/PR3913/tutorials/linear/diet/index.html b/previews/PR3913/tutorials/linear/diet/index.html index 3b365e3c610..783192aaa2b 100644 --- a/previews/PR3913/tutorials/linear/diet/index.html +++ b/previews/PR3913/tutorials/linear/diet/index.html @@ -11,7 +11,7 @@ \min & \sum\limits_{f \in F} c_f x_f \\ \text{s.t.}\ \ & l_m \le \sum\limits_{f \in F} a_{m,f} x_f \le u_m, && \forall m \in M \\ & x_f \ge 0, && \forall f \in F. -\end{aligned}\]

    In the rest of this tutorial, we will create and solve this problem in JuMP, and learn what we should cook for dinner.

    Data

    First, we need some data for the problem. For this tutorial, we'll write CSV files to a temporary directory from Julia. If you have existing files, you could change the filenames to point to them instead.

    dir = mktempdir()
    "/tmp/jl_0qTiI3"

    The first file is a list of foods with their macro-nutrient profile:

    food_csv_filename = joinpath(dir, "diet_foods.csv")
+\end{aligned}\]
    In the rest of this tutorial, we will create and solve this problem in JuMP, and learn what we should cook for dinner.
    Data
    First, we need some data for the problem. For this tutorial, we'll write CSV files to a temporary directory from Julia. If you have existing files, you could change the filenames to point to them instead.
    dir = mktempdir()
    "/tmp/jl_QO9QC3"
    The first file is a list of foods with their macro-nutrient profile:
    food_csv_filename = joinpath(dir, "diet_foods.csv")
 open(food_csv_filename, "w") do io
     write(
         io,
@@ -103,7 +103,7 @@
   Dual objective value : 1.18289e+01
 
 * Work counters
-  Solve time (sec)   : 1.99795e-04
+  Solve time (sec)   : 2.08855e-04
   Simplex iterations : 6
   Barrier iterations : 0
   Node count         : -1
@@ -142,8 +142,8 @@
   Dual objective value : 3.56146e+00
 
 * Work counters
-  Solve time (sec)   : 1.39713e-04
+  Solve time (sec)   : 1.31845e-04
   Simplex iterations : 0
   Barrier iterations : 0
   Node count         : -1
-
    There exists no feasible solution to our problem. Looks like we're stuck eating ice cream for dinner.
    Next steps
    • You can delete a constraint using delete(model, dairy_constraint). Can you add a different constraint to provide a diet with less dairy?
    • Some food items (like hamburgers) are discrete. You can use set_integer to force a variable to take integer values. What happens to the solution if you do?
    
+

    There exists no feasible solution to our problem. Looks like we're stuck eating ice cream for dinner.

    Next steps

    • You can delete a constraint using delete(model, dairy_constraint). Can you add a different constraint to provide a diet with less dairy?
    • Some food items (like hamburgers) are discrete. You can use set_integer to force a variable to take integer values. What happens to the solution if you do?
    diff --git a/previews/PR3913/tutorials/linear/facility_location/18832766.svg b/previews/PR3913/tutorials/linear/facility_location/cb358076.svg similarity index 81% rename from previews/PR3913/tutorials/linear/facility_location/18832766.svg rename to previews/PR3913/tutorials/linear/facility_location/cb358076.svg index e2be6bdd137..8d3927bc9fc 100644 --- a/previews/PR3913/tutorials/linear/facility_location/18832766.svg +++ b/previews/PR3913/tutorials/linear/facility_location/cb358076.svg @@ -1,61 +1,61 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/facility_location/42b7f33e.svg b/previews/PR3913/tutorials/linear/facility_location/d4f1b99a.svg similarity index 79% rename from previews/PR3913/tutorials/linear/facility_location/42b7f33e.svg rename to previews/PR3913/tutorials/linear/facility_location/d4f1b99a.svg index 3914afeb727..6ea25a97a3a 100644 --- a/previews/PR3913/tutorials/linear/facility_location/42b7f33e.svg +++ b/previews/PR3913/tutorials/linear/facility_location/d4f1b99a.svg @@ -1,69 +1,69 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/facility_location/86d4cc0f.svg b/previews/PR3913/tutorials/linear/facility_location/eabed534.svg similarity index 80% rename from previews/PR3913/tutorials/linear/facility_location/86d4cc0f.svg rename to previews/PR3913/tutorials/linear/facility_location/eabed534.svg index ec5df9b5260..ac99d57f46f 100644 --- a/previews/PR3913/tutorials/linear/facility_location/86d4cc0f.svg +++ b/previews/PR3913/tutorials/linear/facility_location/eabed534.svg @@ -1,57 +1,57 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/facility_location/96d80ca9.svg b/previews/PR3913/tutorials/linear/facility_location/f2db4430.svg similarity index 79% rename from previews/PR3913/tutorials/linear/facility_location/96d80ca9.svg rename to previews/PR3913/tutorials/linear/facility_location/f2db4430.svg index 0ac8d5ee822..5e8fcc999da 100644 --- a/previews/PR3913/tutorials/linear/facility_location/96d80ca9.svg +++ b/previews/PR3913/tutorials/linear/facility_location/f2db4430.svg @@ -1,69 +1,69 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/facility_location/index.html b/previews/PR3913/tutorials/linear/facility_location/index.html index a2b29d3c2d8..ebb52416f88 100644 --- a/previews/PR3913/tutorials/linear/facility_location/index.html +++ b/previews/PR3913/tutorials/linear/facility_location/index.html @@ -51,7 +51,7 @@ markersize = 6, markerstrokecolor = :red, markerstrokewidth = 2, -)Example block output

    JuMP implementation

    Create a JuMP model

    model = Model(HiGHS.Optimizer)
+)
    Example block output

    JuMP implementation

    Create a JuMP model

    model = Model(HiGHS.Optimizer)
 set_silent(model)
 @variable(model, y[1:n], Bin);
 @variable(model, x[1:m, 1:n], Bin);
@@ -94,7 +94,7 @@
     end
 end
 
-p
    Example block output

    Capacitated facility location

    Problem formulation

    The capacitated variant introduces a capacity constraint on each facility, that is, clients have a certain level of demand to be served, while each facility only has finite capacity which cannot be exceeded.

    Specifically,

    • The demand of client $i$ is denoted by $a_{i} \geq 0$
    • The capacity of facility $j$ is denoted by $q_{j} \geq 0$

    The capacity constraints then write

    \[\begin{aligned} +pExample block output

    Capacitated facility location

    Problem formulation

    The capacitated variant introduces a capacity constraint on each facility, that is, clients have a certain level of demand to be served, while each facility only has finite capacity which cannot be exceeded.

    Specifically,

    • The demand of client $i$ is denoted by $a_{i} \geq 0$
    • The capacity of facility $j$ is denoted by $q_{j} \geq 0$

    The capacity constraints then write

    \[\begin{aligned} \sum_{i} a_{i} x_{i, j} &\leq q_{j} y_{j} && \forall j \in N \end{aligned}\]

    Note that, if $y_{j}$ is set to $0$, the capacity constraint above automatically forces $x_{i, j}$ to $0$.

    Thus, the capacitated facility location can be formulated as follows

    \[\begin{aligned} \min_{x, y} \ \ \ & @@ -126,7 +126,7 @@ markersize = q, markerstrokecolor = :red, markerstrokewidth = 2, -)Example block output

    JuMP implementation

    Create a JuMP model

    model = Model(HiGHS.Optimizer)
+)
    Example block output

    JuMP implementation

    Create a JuMP model

    model = Model(HiGHS.Optimizer)
 set_silent(model)
 @variable(model, y[1:n], Bin);
 @variable(model, x[1:m, 1:n], Bin);
@@ -169,4 +169,4 @@
     end
 end
 
-p
    Example block output +pExample block output diff --git a/previews/PR3913/tutorials/linear/factory_schedule/bc43d3ce.svg b/previews/PR3913/tutorials/linear/factory_schedule/3434ebab.svg similarity index 78% rename from previews/PR3913/tutorials/linear/factory_schedule/bc43d3ce.svg rename to previews/PR3913/tutorials/linear/factory_schedule/3434ebab.svg index df83bf65dfb..3274804e0e4 100644 --- a/previews/PR3913/tutorials/linear/factory_schedule/bc43d3ce.svg +++ b/previews/PR3913/tutorials/linear/factory_schedule/3434ebab.svg @@ -1,162 +1,162 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/factory_schedule/a152d491.svg b/previews/PR3913/tutorials/linear/factory_schedule/b4a6db29.svg similarity index 85% rename from previews/PR3913/tutorials/linear/factory_schedule/a152d491.svg rename to previews/PR3913/tutorials/linear/factory_schedule/b4a6db29.svg index 2ab46646a7e..46f6631e1e8 100644 --- a/previews/PR3913/tutorials/linear/factory_schedule/a152d491.svg +++ b/previews/PR3913/tutorials/linear/factory_schedule/b4a6db29.svg @@ -1,81 +1,81 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/factory_schedule/244add1b.svg b/previews/PR3913/tutorials/linear/factory_schedule/f4e04e03.svg similarity index 78% rename from previews/PR3913/tutorials/linear/factory_schedule/244add1b.svg rename to previews/PR3913/tutorials/linear/factory_schedule/f4e04e03.svg index 719a9fb2170..ef80abb3ec0 100644 --- a/previews/PR3913/tutorials/linear/factory_schedule/244add1b.svg +++ b/previews/PR3913/tutorials/linear/factory_schedule/f4e04e03.svg @@ -1,160 +1,160 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/factory_schedule/index.html b/previews/PR3913/tutorials/linear/factory_schedule/index.html index 13362336d2c..fea4a6df4f0 100644 --- a/previews/PR3913/tutorials/linear/factory_schedule/index.html +++ b/previews/PR3913/tutorials/linear/factory_schedule/index.html @@ -126,7 +126,7 @@ ylabel = "Production", legend = :topleft, color = ["#20326c" "#4063d8" "#a0b1ec"], -)Example block output

    Note that we don't have any unmet demand.

    What happens if demand increases?

    Let's run an experiment by increasing the demand by 50% in all time periods:

    demand_df.demand .*= 1.5
    12-element Vector{Float64}:
+)
    Example block output

    Note that we don't have any unmet demand.

    What happens if demand increases?

    Let's run an experiment by increasing the demand by 50% in all time periods:

    demand_df.demand .*= 1.5
    12-element Vector{Float64}:
  180000.0
  150000.0
  195000.0
@@ -146,7 +146,7 @@
     ylabel = "Production",
     legend = :topleft,
     color = ["#20326c" "#4063d8" "#a0b1ec"],
-)
    Example block output

    Uh oh, we can't satisfy all of the demand.

    How sensitive is the solution to changes in variable cost?

    Let's run another experiment, this time seeing how the optimal objective value changes as we vary the variable costs of each factory.

    First though, let's reset the demand to it's original level:

    demand_df.demand ./= 1.5;

    For our experiment, we're going to scale the variable costs of both factories by a set of values from 0.0 to 1.5:

    scale_factors = 0:0.1:1.5
    0.0:0.1:1.5

    At a high level, we're going to loop over the scale factors for A, then the scale factors for B, rescale the input data, call our solve_factory_scheduling example, and then store the optimal objective value in the following cost matrix:

    cost = zeros(length(scale_factors), length(scale_factors));

    Because we're modifying factory_df in-place, we need to store the original variable costs in a new column:

    factory_df[!, :old_variable_cost] = copy(factory_df.variable_cost);

    Then, we need a function to scale the :variable_cost column for a particular factory by a value scale:

    function scale_variable_cost(df, factory, scale)
+)
    Example block output

    Uh oh, we can't satisfy all of the demand.

    How sensitive is the solution to changes in variable cost?

    Let's run another experiment, this time seeing how the optimal objective value changes as we vary the variable costs of each factory.

    First though, let's reset the demand to it's original level:

    demand_df.demand ./= 1.5;

    For our experiment, we're going to scale the variable costs of both factories by a set of values from 0.0 to 1.5:

    scale_factors = 0:0.1:1.5
    0.0:0.1:1.5

    At a high level, we're going to loop over the scale factors for A, then the scale factors for B, rescale the input data, call our solve_factory_scheduling example, and then store the optimal objective value in the following cost matrix:

    cost = zeros(length(scale_factors), length(scale_factors));

    Because we're modifying factory_df in-place, we need to store the original variable costs in a new column:

    factory_df[!, :old_variable_cost] = copy(factory_df.variable_cost);

    Then, we need a function to scale the :variable_cost column for a particular factory by a value scale:

    function scale_variable_cost(df, factory, scale)
     rows = df.factory .== factory
     df[rows, :variable_cost] .=
         round.(Int, df[rows, :old_variable_cost] .* scale)
@@ -163,4 +163,4 @@
     cost;
     xlabel = "Scale of factory A",
     ylabel = "Scale of factory B",
-)
    Example block output

    What can you infer from the solution?

    Info

    The Power Systems tutorial explains a number of other ways you can structure a problem to perform a parametric analysis of the solution. In particular, you can use in-place modification to reduce the time it takes to build and solve the resulting models.

    +)Example block output

    What can you infer from the solution?

    Info

    The Power Systems tutorial explains a number of other ways you can structure a problem to perform a parametric analysis of the solution. In particular, you can use in-place modification to reduce the time it takes to build and solve the resulting models.

    diff --git a/previews/PR3913/tutorials/linear/finance/index.html b/previews/PR3913/tutorials/linear/finance/index.html index 2e3735dbd74..1f27381cb3c 100644 --- a/previews/PR3913/tutorials/linear/finance/index.html +++ b/previews/PR3913/tutorials/linear/finance/index.html @@ -50,4 +50,4 @@ 1.0 -0.0 -0.0 - 0.0 + 0.0 diff --git a/previews/PR3913/tutorials/linear/geographic_clustering/index.html b/previews/PR3913/tutorials/linear/geographic_clustering/index.html index c6c1d209f06..32b7566b29f 100644 --- a/previews/PR3913/tutorials/linear/geographic_clustering/index.html +++ b/previews/PR3913/tutorials/linear/geographic_clustering/index.html @@ -135,4 +135,4 @@ 5 │ San Francisco, CA 0.837 37.7749 -122.419 3.0 6 │ El Paso, TX 0.674 31.7775 -106.442 3.0 -sum(group.population) = 9.261000000000001 +sum(group.population) = 9.261000000000001 diff --git a/previews/PR3913/tutorials/linear/introduction/index.html b/previews/PR3913/tutorials/linear/introduction/index.html index 6c363e651aa..e36ceb83b28 100644 --- a/previews/PR3913/tutorials/linear/introduction/index.html +++ b/previews/PR3913/tutorials/linear/introduction/index.html @@ -7,4 +7,4 @@ \min_{x \in \mathbb{R}^n} & \sum\limits_{i=1}^n c_i x_i \\ \;\;\text{s.t.} & l_j \le \sum\limits_{i=1}^n a_{ij} x_i \le u_j & j = 1 \ldots m \\ & l_i \le x_i \le u_i & i = 1 \ldots n. -\end{align}\]

    The most important thing to note is that all terms are of the form coefficient * variable, and that there are no nonlinear terms or multiplications between variables.

    Mixed-integer linear programs (MILPs) are extensions of linear programs in which some (or all) of the decision variables take discrete values.

    How to choose a solver

    Almost all solvers support linear programs; look for "LP" in the list of Supported solvers. However, fewer solvers support mixed-integer linear programs. Solvers supporting discrete variables start with "(MI)" in the list of Supported solvers.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    • The following tutorials are worked examples that present a problem in words, then formulate it in mathematics, and then solve it in JuMP. This usually involves some sort of visualization of the solution. Start here if you are new to JuMP.
    • The Tips and tricks tutorial contains a number of helpful reformulations and tricks you can use when modeling linear programs. Look here if you are stuck trying to formulate a problem as a linear program.
    • The Sensitivity analysis of a linear program tutorial explains how to create sensitivity reports like those produced by the Excel Solver.
    • The Callbacks tutorial explains how to write a variety of solver-independent callbacks. Look here if you want to write a callback.
    • The remaining tutorials are less verbose and styled in the form of short code examples. These tutorials have less explanation, but may contain useful code snippets, particularly if they are similar to a problem you are trying to solve.
    +\end{align}\]

    The most important thing to note is that all terms are of the form coefficient * variable, and that there are no nonlinear terms or multiplications between variables.

    Mixed-integer linear programs (MILPs) are extensions of linear programs in which some (or all) of the decision variables take discrete values.

    How to choose a solver

    Almost all solvers support linear programs; look for "LP" in the list of Supported solvers. However, fewer solvers support mixed-integer linear programs. Solvers supporting discrete variables start with "(MI)" in the list of Supported solvers.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    • The following tutorials are worked examples that present a problem in words, then formulate it in mathematics, and then solve it in JuMP. This usually involves some sort of visualization of the solution. Start here if you are new to JuMP.
    • The Tips and tricks tutorial contains a number of helpful reformulations and tricks you can use when modeling linear programs. Look here if you are stuck trying to formulate a problem as a linear program.
    • The Sensitivity analysis of a linear program tutorial explains how to create sensitivity reports like those produced by the Excel Solver.
    • The Callbacks tutorial explains how to write a variety of solver-independent callbacks. Look here if you want to write a callback.
    • The remaining tutorials are less verbose and styled in the form of short code examples. These tutorials have less explanation, but may contain useful code snippets, particularly if they are similar to a problem you are trying to solve.
    diff --git a/previews/PR3913/tutorials/linear/knapsack/index.html b/previews/PR3913/tutorials/linear/knapsack/index.html index d2cd76f03ce..4b6af3afb82 100644 --- a/previews/PR3913/tutorials/linear/knapsack/index.html +++ b/previews/PR3913/tutorials/linear/knapsack/index.html @@ -49,7 +49,7 @@ Dual objective value : NaN * Work counters - Solve time (sec) : 4.98533e-04 + Solve time (sec) : 5.15938e-04 Simplex iterations : 1 Barrier iterations : -1 Node count : 1 @@ -84,4 +84,4 @@ solve_knapsack_problem(; profit = profit, weight = weight, capacity = capacity)
    3-element Vector{Int64}:
  1
  4
- 5

    We observe that the chosen items (1, 4, and 5) have the best profit to weight ratio in this particular example.

    Next steps

    Here are some things to try next:

    • Call the function with different data. What happens as the capacity increases?
    • What happens if the profit and weight vectors are different lengths?
    • Instead of creating a binary variable with Bin, we could have written @variable(model, 0 <= x[1:n] <= 1, Int). Verify that this formulation finds the same solution. What happens if we are allowed to take more than one of each item?
    + 5

    We observe that the chosen items (1, 4, and 5) have the best profit to weight ratio in this particular example.

    Next steps

    Here are some things to try next:

    • Call the function with different data. What happens as the capacity increases?
    • What happens if the profit and weight vectors are different lengths?
    • Instead of creating a binary variable with Bin, we could have written @variable(model, 0 <= x[1:n] <= 1, Int). Verify that this formulation finds the same solution. What happens if we are allowed to take more than one of each item?
    diff --git a/previews/PR3913/tutorials/linear/lp_sensitivity/index.html b/previews/PR3913/tutorials/linear/lp_sensitivity/index.html index b945282af82..045f59284b3 100644 --- a/previews/PR3913/tutorials/linear/lp_sensitivity/index.html +++ b/previews/PR3913/tutorials/linear/lp_sensitivity/index.html @@ -40,11 +40,11 @@ c3 : 0.00000e+00 * Work counters - Solve time (sec) : 2.40564e-04 + Solve time (sec) : 2.25544e-04 Simplex iterations : 2 Barrier iterations : 0 Node count : -1 -

    Can you identify:

    • The objective coefficient of each variable?
    • The right-hand side of each constraint?
    • The optimal primal and dual solutions?

    Sensitivity reports

    Now let's call lp_sensitivity_report:

    report = lp_sensitivity_report(model)
    SensitivityReport{Float64}(Dict{ConstraintRef, Tuple{Float64, Float64}}(c2 : 7 x + 12 y ≥ 120 => (-3.3333333333333335, 4.666666666666667), c1 : 6 x + 8 y ≥ 100 => (-4.0, 2.857142857142857), y ≤ 3 => (-1.75, Inf), z ≤ 1 => (-Inf, Inf), x ≥ 0 => (-Inf, 15.0), c3 : x + y ≤ 20 => (-3.75, Inf), y ≥ 0 => (-Inf, 1.25)), Dict{VariableRef, Tuple{Float64, Float64}}(z => (-Inf, 1.0), y => (-4.0, 0.5714285714285714), x => (-0.3333333333333333, 3.0)))

    It returns a SensitivityReport object, which maps:

    • Every variable reference to a tuple (d_lo, d_hi)::Tuple{Float64,Float64}, explaining how much the objective coefficient of the corresponding variable can change by, such that the original basis remains optimal.
    • Every constraint reference to a tuple (d_lo, d_hi)::Tuple{Float64,Float64}, explaining how much the right-hand side of the corresponding constraint can change by, such that the basis remains optimal.

    Both tuples are relative, rather than absolute. So, given an objective coefficient of 1.0 and a tuple (-0.5, 0.5), the objective coefficient can range between 1.0 - 0.5 an 1.0 + 0.5.

    For example:

    report[x]
    (-0.3333333333333333, 3.0)

    indicates that the objective coefficient on x, that is, 12, can decrease by -0.333 or increase by 3.0 and the primal solution (15, 1.25) will remain optimal. In addition:

    report[c1]
    (-4.0, 2.857142857142857)

    means that the right-hand side of the c1 constraint (100), can decrease by 4 units, or increase by 2.85 units, and the primal solution (15, 1.25) will remain optimal.

    Variable sensitivity

    By themselves, the tuples aren't informative. Let's put them in context by collating a range of other information about a variable:

    function variable_report(xi)
+

    Can you identify:

    • The objective coefficient of each variable?
    • The right-hand side of each constraint?
    • The optimal primal and dual solutions?

    Sensitivity reports

    Now let's call lp_sensitivity_report:

    report = lp_sensitivity_report(model)
    SensitivityReport{Float64}(Dict{ConstraintRef, Tuple{Float64, Float64}}(c1 : 6 x + 8 y ≥ 100 => (-4.0, 2.857142857142857), c2 : 7 x + 12 y ≥ 120 => (-3.3333333333333335, 4.666666666666667), c3 : x + y ≤ 20 => (-3.75, Inf), x ≥ 0 => (-Inf, 15.0), y ≥ 0 => (-Inf, 1.25), y ≤ 3 => (-1.75, Inf), z ≤ 1 => (-Inf, Inf)), Dict{VariableRef, Tuple{Float64, Float64}}(y => (-4.0, 0.5714285714285714), x => (-0.3333333333333333, 3.0), z => (-Inf, 1.0)))

    It returns a SensitivityReport object, which maps:

    • Every variable reference to a tuple (d_lo, d_hi)::Tuple{Float64,Float64}, explaining how much the objective coefficient of the corresponding variable can change by, such that the original basis remains optimal.
    • Every constraint reference to a tuple (d_lo, d_hi)::Tuple{Float64,Float64}, explaining how much the right-hand side of the corresponding constraint can change by, such that the basis remains optimal.

    Both tuples are relative, rather than absolute. So, given an objective coefficient of 1.0 and a tuple (-0.5, 0.5), the objective coefficient can range between 1.0 - 0.5 an 1.0 + 0.5.

    For example:

    report[x]
    (-0.3333333333333333, 3.0)

    indicates that the objective coefficient on x, that is, 12, can decrease by -0.333 or increase by 3.0 and the primal solution (15, 1.25) will remain optimal. In addition:

    report[c1]
    (-4.0, 2.857142857142857)

    means that the right-hand side of the c1 constraint (100), can decrease by 4 units, or increase by 2.85 units, and the primal solution (15, 1.25) will remain optimal.

    Variable sensitivity

    By themselves, the tuples aren't informative. Let's put them in context by collating a range of other information about a variable:

    function variable_report(xi)
     return (
         name = name(xi),
         lower_bound = has_lower_bound(xi) ? lower_bound(xi) : -Inf,
@@ -71,4 +71,4 @@
 c1_report = constraint_report(c1)
    (name = "c1", value = 100.0, rhs = 100.0, slack = 0.0, shadow_price = -0.25, allowed_decrease = -4.0, allowed_increase = 2.857142857142857)

    That's a bit hard to read, so let's call this on every variable in the model and put things into a DataFrame:

    constraint_df = DataFrames.DataFrame(
     constraint_report(ci) for (F, S) in list_of_constraint_types(model) for
     ci in all_constraints(model, F, S) if F == AffExpr
-)
    3×7 DataFrame
    Rownamevaluerhsslackshadow_priceallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64
    1c1100.0100.00.0-0.25-4.02.85714
    2c2120.0120.00.0-1.5-3.333334.66667
    3c316.2520.03.750.0-3.75Inf

    Analysis questions

    Now we can use these dataframes to ask questions of the solution.

    For example, we can find basic variables by looking for variables with a reduced cost of 0:

    basic = filter(row -> iszero(row.reduced_cost), variable_df)
    2×8 DataFrame
    Rownamelower_boundvalueupper_boundreduced_costobj_coefficientallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64Float64
    1x0.015.0Inf0.012.0-0.3333333.0
    2y0.01.253.00.020.0-4.00.571429

    and non-basic variables by looking for non-zero reduced costs:

    non_basic = filter(row -> !iszero(row.reduced_cost), variable_df)
    1×8 DataFrame
    Rownamelower_boundvalueupper_boundreduced_costobj_coefficientallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64Float64
    1z-Inf1.01.0-1.0-1.0-Inf1.0

    we can also find constraints that are binding by looking for zero slacks:

    binding = filter(row -> iszero(row.slack), constraint_df)
    2×7 DataFrame
    Rownamevaluerhsslackshadow_priceallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64
    1c1100.0100.00.0-0.25-4.02.85714
    2c2120.0120.00.0-1.5-3.333334.66667

    or non-zero shadow prices:

    binding2 = filter(row -> !iszero(row.shadow_price), constraint_df)
    2×7 DataFrame
    Rownamevaluerhsslackshadow_priceallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64
    1c1100.0100.00.0-0.25-4.02.85714
    2c2120.0120.00.0-1.5-3.333334.66667
    +)
    3×7 DataFrame
    Rownamevaluerhsslackshadow_priceallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64
    1c1100.0100.00.0-0.25-4.02.85714
    2c2120.0120.00.0-1.5-3.333334.66667
    3c316.2520.03.750.0-3.75Inf

    Analysis questions

    Now we can use these dataframes to ask questions of the solution.

    For example, we can find basic variables by looking for variables with a reduced cost of 0:

    basic = filter(row -> iszero(row.reduced_cost), variable_df)
    2×8 DataFrame
    Rownamelower_boundvalueupper_boundreduced_costobj_coefficientallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64Float64
    1x0.015.0Inf0.012.0-0.3333333.0
    2y0.01.253.00.020.0-4.00.571429

    and non-basic variables by looking for non-zero reduced costs:

    non_basic = filter(row -> !iszero(row.reduced_cost), variable_df)
    1×8 DataFrame
    Rownamelower_boundvalueupper_boundreduced_costobj_coefficientallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64Float64
    1z-Inf1.01.0-1.0-1.0-Inf1.0

    we can also find constraints that are binding by looking for zero slacks:

    binding = filter(row -> iszero(row.slack), constraint_df)
    2×7 DataFrame
    Rownamevaluerhsslackshadow_priceallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64
    1c1100.0100.00.0-0.25-4.02.85714
    2c2120.0120.00.0-1.5-3.333334.66667

    or non-zero shadow prices:

    binding2 = filter(row -> !iszero(row.shadow_price), constraint_df)
    2×7 DataFrame
    Rownamevaluerhsslackshadow_priceallowed_decreaseallowed_increase
    StringFloat64Float64Float64Float64Float64Float64
    1c1100.0100.00.0-0.25-4.02.85714
    2c2120.0120.00.0-1.5-3.333334.66667
    diff --git a/previews/PR3913/tutorials/linear/mip_duality/index.html b/previews/PR3913/tutorials/linear/mip_duality/index.html index 18a875223bb..75e20e61fb6 100644 --- a/previews/PR3913/tutorials/linear/mip_duality/index.html +++ b/previews/PR3913/tutorials/linear/mip_duality/index.html @@ -113,4 +113,4 @@ g[2] ≤ 1000 w ≤ 200 dispatch[1] binary - dispatch[2] binary + dispatch[2] binary diff --git a/previews/PR3913/tutorials/linear/multi/index.html b/previews/PR3913/tutorials/linear/multi/index.html index 7e4ecd367cc..58eedfb0393 100644 --- a/previews/PR3913/tutorials/linear/multi/index.html +++ b/previews/PR3913/tutorials/linear/multi/index.html @@ -118,7 +118,7 @@ INNER JOIN locations b ON a.type = 'origin' AND b.type = 'destination' """, -)
    SQLite.Query{false}(SQLite.Stmt(SQLite.DB("/home/runner/work/JuMP.jl/JuMP.jl/docs/build/tutorials/linear/multi.sqlite"), Base.RefValue{Ptr{SQLite.C.sqlite3_stmt}}(Ptr{SQLite.C.sqlite3_stmt} @0x00000000449ef898), Dict{Int64, Any}()), Base.RefValue{Int32}(100), [:origin, :destination], Type[Union{Missing, String}, Union{Missing, String}], Dict(:origin => 1, :destination => 2), Base.RefValue{Int64}(0))

    With a constraint that we cannot send more than 625 units between each pair:

    for r in Tables.rows(od_pairs)
+)
    SQLite.Query{false}(SQLite.Stmt(SQLite.DB("/home/runner/work/JuMP.jl/JuMP.jl/docs/build/tutorials/linear/multi.sqlite"), Base.RefValue{Ptr{SQLite.C.sqlite3_stmt}}(Ptr{SQLite.C.sqlite3_stmt} @0x0000000050392698), Dict{Int64, Any}()), Base.RefValue{Int32}(100), [:origin, :destination], Type[Union{Missing, String}, Union{Missing, String}], Dict(:origin => 1, :destination => 2), Base.RefValue{Int64}(0))

    With a constraint that we cannot send more than 625 units between each pair:

    for r in Tables.rows(od_pairs)
     @constraint(model, sum(x[r.origin, r.destination, :]) <= 625)
 end

    Solution

    Finally, we can optimize the model:

    optimize!(model)
 Test.@test is_solved_and_feasible(model)
@@ -139,7 +139,7 @@
   Dual objective value : 2.25700e+05
 
 * Work counters
-  Solve time (sec)   : 6.32763e-04
+  Solve time (sec)   : 6.79493e-04
   Simplex iterations : 54
   Barrier iterations : 0
   Node count         : -1
@@ -170,4 +170,4 @@
 PITT WIN    75   250    .
 PITT STL   400    25   200
 PITT FRE    .    450   100
-PITT LAF   250   125    .
    +PITT LAF 250 125 . diff --git a/previews/PR3913/tutorials/linear/multi_commodity_network/index.html b/previews/PR3913/tutorials/linear/multi_commodity_network/index.html index a3ba8ff3bb1..45d7f12da7f 100644 --- a/previews/PR3913/tutorials/linear/multi_commodity_network/index.html +++ b/previews/PR3913/tutorials/linear/multi_commodity_network/index.html @@ -87,7 +87,7 @@ Dual objective value : 1.43228e+02 * Work counters - Solve time (sec) : 3.41177e-04 + Solve time (sec) : 3.30210e-04 Simplex iterations : 8 Barrier iterations : 0 Node count : -1 @@ -95,4 +95,4 @@ df_supply.x_supply = value.(df_supply.x_supply);

    and display the optimal solution for flows:

    DataFrames.select(
     filter!(row -> row.x_flow > 0.0, df_shipping),
     [:origin, :destination, :product, :x_flow],
-)
    9×4 DataFrame
    Roworigindestinationproductx_flow
    StringStringStringFloat64
    1waikatoaucklandmilk10.0
    2waikatowellingtonmilk2.0
    3taurangaaucklandmilk2.0
    4taurangawaikatomilk2.0
    5christchurchaucklandmilk4.0
    6aucklandchristchurchkiwifruit4.0
    7waikatoaucklandkiwifruit20.0
    8waikatowellingtonkiwifruit2.0
    9taurangawaikatokiwifruit22.0
    +)
    9×4 DataFrame
    Roworigindestinationproductx_flow
    StringStringStringFloat64
    1waikatoaucklandmilk10.0
    2waikatowellingtonmilk2.0
    3taurangaaucklandmilk2.0
    4taurangawaikatomilk2.0
    5christchurchaucklandmilk4.0
    6aucklandchristchurchkiwifruit4.0
    7waikatoaucklandkiwifruit20.0
    8waikatowellingtonkiwifruit2.0
    9taurangawaikatokiwifruit22.0
    diff --git a/previews/PR3913/tutorials/linear/multi_objective_examples/index.html b/previews/PR3913/tutorials/linear/multi_objective_examples/index.html index bab55ece98a..9810a718134 100644 --- a/previews/PR3913/tutorials/linear/multi_objective_examples/index.html +++ b/previews/PR3913/tutorials/linear/multi_objective_examples/index.html @@ -29,7 +29,7 @@ Objective bound : [0.00000e+00,-9.00000e+00] * Work counters - Solve time (sec) : 1.15418e-03 + Solve time (sec) : 1.17087e-03 
    for i in 1:result_count(model)
     @assert is_solved_and_feasible(model; result = i)
     print(i, ": z = ", round.(Int, objective_value(model; result = i)), " | ")
@@ -62,7 +62,7 @@
   Objective bound    : [6.00000e+00,7.00000e+00]
 
 * Work counters
-  Solve time (sec)   : 7.46894e-03
+  Solve time (sec)   : 9.66597e-03
 
    for i in 1:result_count(model)
     @assert is_solved_and_feasible(model; result = i)
     print(i, ": z = ", round.(Int, objective_value(model; result = i)), " | ")
@@ -115,7 +115,7 @@
   Objective bound    : [8.00000e+00,4.00000e+00]
 
 * Work counters
-  Solve time (sec)   : 5.30386e-03
+  Solve time (sec)   : 5.35893e-03
 
    for i in 1:result_count(model)
     @assert is_solved_and_feasible(model; result = i)
     print(i, ": z = ", round.(Int, objective_value(model; result = i)), " | ")
@@ -129,4 +129,4 @@
 end
    1: z = [8, 9] | Path: 1->2 2->4 4->6
 2: z = [10, 7] | Path: 1->2 2->5 5->6
 3: z = [11, 5] | Path: 1->2 2->6
-4: z = [13, 4] | Path: 1->3 3->4 4->6
    +4: z = [13, 4] | Path: 1->3 3->4 4->6 diff --git a/previews/PR3913/tutorials/linear/multi_objective_knapsack/368eaf8b.svg b/previews/PR3913/tutorials/linear/multi_objective_knapsack/0a5f4828.svg similarity index 87% rename from previews/PR3913/tutorials/linear/multi_objective_knapsack/368eaf8b.svg rename to previews/PR3913/tutorials/linear/multi_objective_knapsack/0a5f4828.svg index 9f0956c83ae..d9ce5674d73 100644 --- a/previews/PR3913/tutorials/linear/multi_objective_knapsack/368eaf8b.svg +++ b/previews/PR3913/tutorials/linear/multi_objective_knapsack/0a5f4828.svg @@ -1,53 +1,53 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/multi_objective_knapsack/968541ac.svg b/previews/PR3913/tutorials/linear/multi_objective_knapsack/6b5572c3.svg similarity index 83% rename from previews/PR3913/tutorials/linear/multi_objective_knapsack/968541ac.svg rename to previews/PR3913/tutorials/linear/multi_objective_knapsack/6b5572c3.svg index 624638af8ff..c2496184b67 100644 --- a/previews/PR3913/tutorials/linear/multi_objective_knapsack/968541ac.svg +++ b/previews/PR3913/tutorials/linear/multi_objective_knapsack/6b5572c3.svg @@ -1,55 +1,55 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/multi_objective_knapsack/index.html b/previews/PR3913/tutorials/linear/multi_objective_knapsack/index.html index 964a176b992..ea20f9c8382 100644 --- a/previews/PR3913/tutorials/linear/multi_objective_knapsack/index.html +++ b/previews/PR3913/tutorials/linear/multi_objective_knapsack/index.html @@ -25,7 +25,7 @@ xlabel = "Profit", ylabel = "Desire", legend = false, -)Example block output

    The goal of the bi-objective knapsack problem is to choose a subset which maximizes both objectives.

    JuMP formulation

    Our JuMP formulation is a direct translation of the mathematical formulation:

    model = Model()
+)
    Example block output

    The goal of the bi-objective knapsack problem is to choose a subset which maximizes both objectives.

    JuMP formulation

    Our JuMP formulation is a direct translation of the mathematical formulation:

    model = Model()
 @variable(model, x[1:N], Bin)
 @constraint(model, sum(weight[i] * x[i] for i in 1:N) <= capacity)
 @expression(model, profit_expr, sum(profit[i] * x[i] for i in 1:N))
@@ -50,7 +50,7 @@
   Objective bound    : [9.55000e+02,9.83000e+02]
 
 * Work counters
-  Solve time (sec)   : 9.68990e-02
+  Solve time (sec)   : 9.57360e-02

    There are 9 solutions available. We can also use result_count to see how many solutions are available:

    result_count(model)
    9

    Accessing multiple solutions

    Access the nine different solutions in the model using the result keyword to solution_summary, value, and objective_value:

    solution_summary(model; result = 5)
    * Solver : MOA[algorithm=MultiObjectiveAlgorithms.EpsilonConstraint, optimizer=HiGHS]
 
 * Status
@@ -77,7 +77,7 @@
     Plots.annotate!(y[1] - 1, y[2], (i, 10))
 end
 ideal_point = objective_bound(model)
-Plots.scatter!([ideal_point[1]], [ideal_point[2]]; label = "Ideal point")
    Example block output

    Visualizing the objective space lets the decision maker choose a solution that suits their personal preferences. For example, result #7 is close to the maximum value of profit, but offers significantly higher desirability compared with solutions #8 and #9.

    The set of items that are chosen in solution #7 are:

    items_chosen = [i for i in 1:N if value(x[i]; result = 7) > 0.9]
    11-element Vector{Int64}:
+Plots.scatter!([ideal_point[1]], [ideal_point[2]]; label = "Ideal point")
    Example block output

    Visualizing the objective space lets the decision maker choose a solution that suits their personal preferences. For example, result #7 is close to the maximum value of profit, but offers significantly higher desirability compared with solutions #8 and #9.

    The set of items that are chosen in solution #7 are:

    items_chosen = [i for i in 1:N if value(x[i]; result = 7) > 0.9]
    11-element Vector{Int64}:
   1
   2
   3
@@ -88,4 +88,4 @@
  11
  15
  16
- 17

    Next steps

    MultiObjectiveAlgorithms.jl implements a number of different algorithms. Try solving the same problem using MOA.Dichotomy(). Does it find the same solution?

    + 17

    Next steps

    MultiObjectiveAlgorithms.jl implements a number of different algorithms. Try solving the same problem using MOA.Dichotomy(). Does it find the same solution?

    diff --git a/previews/PR3913/tutorials/linear/multiple_solutions/index.html b/previews/PR3913/tutorials/linear/multiple_solutions/index.html index a4f250917e2..5015d06d514 100644 --- a/previews/PR3913/tutorials/linear/multiple_solutions/index.html +++ b/previews/PR3913/tutorials/linear/multiple_solutions/index.html @@ -42,7 +42,7 @@ Dual objective value : 0.00000e+00 * Work counters - Solve time (sec) : 4.50652e-02 + Solve time (sec) : 4.48790e-02 Simplex iterations : 1587 Barrier iterations : 0 Node count : 255 @@ -69,7 +69,7 @@ Dual objective value : 0.00000e+00 * Work counters - Solve time (sec) : 3.75886e-01 + Solve time (sec) : 3.73572e-01 Simplex iterations : 19526 Barrier iterations : 0 Node count : 4661 @@ -203,4 +203,4 @@ 3 2 1 6 2 0 4 7 + 1 4 9 5 -= 6 7 5 8

    The result is the full list of feasible solutions. So the answer to "how many such squares are there?" turns out to be 20.

    += 6 7 5 8

    The result is the full list of feasible solutions. So the answer to "how many such squares are there?" turns out to be 20.

    diff --git a/previews/PR3913/tutorials/linear/n-queens/index.html b/previews/PR3913/tutorials/linear/n-queens/index.html index f0cab48b9e7..2a30816d052 100644 --- a/previews/PR3913/tutorials/linear/n-queens/index.html +++ b/previews/PR3913/tutorials/linear/n-queens/index.html @@ -23,4 +23,4 @@ 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 - 0 1 0 0 0 0 0 0 + 0 1 0 0 0 0 0 0 diff --git a/previews/PR3913/tutorials/linear/network_flows/index.html b/previews/PR3913/tutorials/linear/network_flows/index.html index 8903cd92162..37dbd05d961 100644 --- a/previews/PR3913/tutorials/linear/network_flows/index.html +++ b/previews/PR3913/tutorials/linear/network_flows/index.html @@ -91,4 +91,4 @@ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 - 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 diff --git a/previews/PR3913/tutorials/linear/piecewise_linear/8d34fc47.svg b/previews/PR3913/tutorials/linear/piecewise_linear/08cb723e.svg similarity index 82% rename from previews/PR3913/tutorials/linear/piecewise_linear/8d34fc47.svg rename to previews/PR3913/tutorials/linear/piecewise_linear/08cb723e.svg index d29ea988f0f..41aefacde2d 100644 --- a/previews/PR3913/tutorials/linear/piecewise_linear/8d34fc47.svg +++ b/previews/PR3913/tutorials/linear/piecewise_linear/08cb723e.svg @@ -1,61 +1,61 @@ - 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+ - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/piecewise_linear/83f88874.svg b/previews/PR3913/tutorials/linear/piecewise_linear/fe59417d.svg similarity index 86% rename from previews/PR3913/tutorials/linear/piecewise_linear/83f88874.svg rename to previews/PR3913/tutorials/linear/piecewise_linear/fe59417d.svg index 4bce39be3b0..04970b4f306 100644 --- a/previews/PR3913/tutorials/linear/piecewise_linear/83f88874.svg +++ b/previews/PR3913/tutorials/linear/piecewise_linear/fe59417d.svg @@ -1,43 +1,43 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/linear/piecewise_linear/index.html b/previews/PR3913/tutorials/linear/piecewise_linear/index.html index 65ded599cec..eb011db3fa5 100644 --- a/previews/PR3913/tutorials/linear/piecewise_linear/index.html +++ b/previews/PR3913/tutorials/linear/piecewise_linear/index.html @@ -7,11 +7,11 @@ import HiGHS import Plots

    Minimizing a convex function (outer approximation)

    If the function you are approximating is convex, and you want to minimize "down" onto it, then you can use an outer approximation.

    For example, $f(x) = x^2$ is a convex function:

    f(x) = x^2
 ∇f(x) = 2 * x
-plot = Plots.plot(f, -2:0.01:2; ylims = (-0.5, 4), label = false, width = 3)
    Example block output

    Because $f$ is convex, we know that for any $x_k$, we have: $f(x) \ge f(x_k) + \nabla f(x_k) \cdot (x - x_k)$

    for x_k in -2:1:2  ## Tip: try changing the number of points x_k
+plot = Plots.plot(f, -2:0.01:2; ylims = (-0.5, 4), label = false, width = 3)
    Example block output

    Because $f$ is convex, we know that for any $x_k$, we have: $f(x) \ge f(x_k) + \nabla f(x_k) \cdot (x - x_k)$

    for x_k in -2:1:2  ## Tip: try changing the number of points x_k
     g = x -> f(x_k) + ∇f(x_k) * (x - x_k)
     Plots.plot!(plot, g, -2:0.01:2; color = :red, label = false, width = 3)
 end
-plot
    Example block output

    We can use these tangent planes as constraints in our model to create an outer approximation of the function. As we add more planes, the error between the true function and the piecewise linear outer approximation decreases.

    Here is the model in JuMP:

    function outer_approximate_x_squared(x̄)
+plot
    Example block output

    We can use these tangent planes as constraints in our model to create an outer approximation of the function. As we add more planes, the error between the true function and the piecewise linear outer approximation decreases.

    Here is the model in JuMP:

    function outer_approximate_x_squared(x̄)
     f(x) = x^2
     ∇f(x) = 2x
     model = Model(HiGHS.Optimizer)
@@ -29,7 +29,7 @@
     ȳ = outer_approximate_x_squared(x̄)
     Plots.scatter!(plot, [x̄], [ȳ]; label = false, color = :black)
 end
-plot
    Example block output
    Note

    This formulation does not work if we want to maximize y.

    Maximizing a concave function (outer approximation)

    The outer approximation also works if we want to maximize "up" into a concave function.

    f(x) = log(x)
+plot
    Example block output
    Note

    This formulation does not work if we want to maximize y.

    Maximizing a concave function (outer approximation)

    The outer approximation also works if we want to maximize "up" into a concave function.

    f(x) = log(x)
 ∇f(x) = 1 / x
 X = 0.1:0.1:1.6
 plot = Plots.plot(
@@ -44,7 +44,7 @@
     g = x -> f(x_k) + ∇f(x_k) * (x - x_k)
     Plots.plot!(plot, g, X; color = :red, label = false, width = 3)
 end
-plot
    Example block output

    Here is the model in JuMP:

    function outer_approximate_log(x̄)
+plot
    Example block output

    Here is the model in JuMP:

    function outer_approximate_log(x̄)
     f(x) = log(x)
     ∇f(x) = 1 / x
     model = Model(HiGHS.Optimizer)
@@ -62,18 +62,18 @@
     ȳ = outer_approximate_log(x̄)
     Plots.scatter!(plot, [x̄], [ȳ]; label = false, color = :black)
 end
-plot
    Example block output
    Note

    This formulation does not work if we want to minimize y.

    Minimizing a convex function (inner approximation)

    Instead of creating an outer approximation, we can also create an inner approximation. For example, given $f(x) = x^2$, we may want to approximate the true function by the red piecewise linear function:

    f(x) = x^2
+plot
    Example block output
    Note

    This formulation does not work if we want to minimize y.

    Minimizing a convex function (inner approximation)

    Instead of creating an outer approximation, we can also create an inner approximation. For example, given $f(x) = x^2$, we may want to approximate the true function by the red piecewise linear function:

    f(x) = x^2
 x̂ = -2:0.8:2  ## Tip: try changing the number of points in x̂
 plot = Plots.plot(f, -2:0.01:2; ylims = (-0.5, 4), label = false, linewidth = 3)
 Plots.plot!(plot, f, x̂; label = false, color = :red, linewidth = 3)
-plot
    Example block output

    To do so, we represent the decision variables $(x, y)$ by the convex combination of a set of discrete points $\{x_k, y_k\}_{k=1}^K$:

    \[\begin{aligned} +plotExample block output

    To do so, we represent the decision variables $(x, y)$ by the convex combination of a set of discrete points $\{x_k, y_k\}_{k=1}^K$:

    \[\begin{aligned} x = \sum\limits_{k=1}^K \lambda_k x_k \\ y = \sum\limits_{k=1}^K \lambda_k y_k \\ \sum\limits_{k=1}^K \lambda_k = 1 \\ \lambda_k \ge 0, k=1,\ldots,k \\ \end{aligned}\]

    The feasible region of the convex combination actually allows any $(x, y)$ point inside this shaded region:

    I = [1, 2, 3, 4, 5, 6, 1]
 Plots.plot!(x̂[I], f.(x̂[I]); fill = (0, 0, "#f004"), width = 0, label = false)
-plot
    Example block output

    Thus, this formulation does not work if we want to maximize $y$.

    Here is the model in JuMP:

    function inner_approximate_x_squared(x̄)
+plot
    Example block output

    Thus, this formulation does not work if we want to maximize $y$.

    Here is the model in JuMP:

    function inner_approximate_x_squared(x̄)
     f(x) = x^2
     ∇f(x) = 2x
     x̂ = -2:0.8:2  ## Tip: try changing the number of points in x̂
@@ -96,13 +96,13 @@
     ȳ = inner_approximate_x_squared(x̄)
     Plots.scatter!(plot, [x̄], [ȳ]; label = false, color = :black)
 end
-plot
    Example block output

    Maximizing a convex function (inner approximation)

    The inner approximation also works if we want to maximize "up" into a concave function.

    f(x) = log(x)
+plot
    Example block output

    Maximizing a convex function (inner approximation)

    The inner approximation also works if we want to maximize "up" into a concave function.

    f(x) = log(x)
 x̂ = 0.1:0.5:1.6  ## Tip: try changing the number of points in x̂
 plot = Plots.plot(f, 0.1:0.01:1.6; label = false, linewidth = 3)
 Plots.plot!(x̂, f.(x̂); linewidth = 3, color = :red, label = false)
 I = [1, 2, 3, 4, 1]
 Plots.plot!(x̂[I], f.(x̂[I]); fill = (0, 0, "#f004"), width = 0, label = false)
-plot
    Example block output

    Here is the model in JuMP:

    function inner_approximate_log(x̄)
+plot
    Example block output

    Here is the model in JuMP:

    function inner_approximate_log(x̄)
     f(x) = log(x)
     x̂ = 0.1:0.5:1.6  ## Tip: try changing the number of points in x̂
     ŷ = f.(x̂)
@@ -124,13 +124,13 @@
     ȳ = inner_approximate_log(x̄)
     Plots.scatter!(plot, [x̄], [ȳ]; label = false, color = :black)
 end
-plot
    Example block output

    Piecewise linear approximation

    If the model is non-convex (or non-concave), then we cannot use an outer approximation, and the inner approximation allows a solution far from the true function. For example, for $f(x) = sin(x)$, we have:

    f(x) = sin(x)
+plot
    Example block output

    Piecewise linear approximation

    If the model is non-convex (or non-concave), then we cannot use an outer approximation, and the inner approximation allows a solution far from the true function. For example, for $f(x) = sin(x)$, we have:

    f(x) = sin(x)
 plot = Plots.plot(f, 0:0.01:2π; label = false)
 x̂ = range(; start = 0, stop = 2π, length = 7)
 Plots.plot!(x̂, f.(x̂); linewidth = 3, color = :red, label = false)
 I = [1, 5, 6, 7, 3, 2, 1]
 Plots.plot!(x̂[I], f.(x̂[I]); fill = (0, 0, "#f004"), width = 0, label = false)
-plot
    Example block output

    We can force the inner approximation to stay on the red line by adding the constraint λ in SOS2(). The SOS2 set is a Special Ordered Set of Type 2, and it ensures that at most two elements of λ can be non-zero, and if they are, that they must be adjacent. This prevents the model from taking a convex combination of points 1 and 5 to end up on the lower boundary of the shaded red area.

    Here is the model in JuMP:

    function piecewise_linear_sin(x̄)
+plot
    Example block output

    We can force the inner approximation to stay on the red line by adding the constraint λ in SOS2(). The SOS2 set is a Special Ordered Set of Type 2, and it ensures that at most two elements of λ can be non-zero, and if they are, that they must be adjacent. This prevents the model from taking a convex combination of points 1 and 5 to end up on the lower boundary of the shaded red area.

    Here is the model in JuMP:

    function piecewise_linear_sin(x̄)
     f(x) = sin(x)
     # Tip: try changing the number of points in x̂
     x̂ = range(; start = 0, stop = 2π, length = 7)
@@ -155,4 +155,4 @@
     ȳ = piecewise_linear_sin(x̄)
     Plots.scatter!(plot, [x̄], [ȳ]; label = false, color = :black)
 end
-plot
    Example block output +plotExample block output diff --git a/previews/PR3913/tutorials/linear/sudoku/index.html b/previews/PR3913/tutorials/linear/sudoku/index.html index 4a8c2c9cd71..102be4f5dbe 100644 --- a/previews/PR3913/tutorials/linear/sudoku/index.html +++ b/previews/PR3913/tutorials/linear/sudoku/index.html @@ -93,4 +93,4 @@ 7 1 3 9 2 4 8 5 6 9 6 1 5 3 7 2 8 4 2 8 7 4 1 9 6 3 5 - 3 4 5 2 8 6 1 7 9

    Which is the same as we found before:

    sol == csp_sol
    true
    + 3 4 5 2 8 6 1 7 9

    Which is the same as we found before:

    sol == csp_sol
    true
    diff --git a/previews/PR3913/tutorials/linear/tips_and_tricks/index.html b/previews/PR3913/tutorials/linear/tips_and_tricks/index.html index 36ecb4f27dc..2671682caf2 100644 --- a/previews/PR3913/tutorials/linear/tips_and_tricks/index.html +++ b/previews/PR3913/tutorials/linear/tips_and_tricks/index.html @@ -70,4 +70,4 @@ y == sum(ŷ[i] * λ[i] for i in 1:N) sum(λ) == 1 λ in SOS2() - end)(x + λ[1] + 0.5 λ[2] - 0.5 λ[4] - λ[5] - 1.5 λ[6] - 2 λ[7] = 0, y - λ[1] - 0.25 λ[2] - 0.25 λ[4] - λ[5] - 2.25 λ[6] - 4 λ[7] = 0, λ[1] + λ[2] + λ[3] + λ[4] + λ[5] + λ[6] + λ[7] = 1, [λ[1], λ[2], λ[3], λ[4], λ[5], λ[6], λ[7]] ∈ MathOptInterface.SOS2{Float64}([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0])) + end)(x + λ[1] + 0.5 λ[2] - 0.5 λ[4] - λ[5] - 1.5 λ[6] - 2 λ[7] = 0, y - λ[1] - 0.25 λ[2] - 0.25 λ[4] - λ[5] - 2.25 λ[6] - 4 λ[7] = 0, λ[1] + λ[2] + λ[3] + λ[4] + λ[5] + λ[6] + λ[7] = 1, [λ[1], λ[2], λ[3], λ[4], λ[5], λ[6], λ[7]] ∈ MathOptInterface.SOS2{Float64}([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0])) diff --git a/previews/PR3913/tutorials/linear/transp/index.html b/previews/PR3913/tutorials/linear/transp/index.html index 48b7bad4882..a9aeb4d4bb5 100644 --- a/previews/PR3913/tutorials/linear/transp/index.html +++ b/previews/PR3913/tutorials/linear/transp/index.html @@ -74,4 +74,4 @@ end
    solve_transportation_problem (generic function with 1 method)

    Solution

    Let's solve and view the solution:

    solve_transportation_problem(data)
            FRA    DET    LAN    WIN    STL    FRE    LAF
 GARY      .      .      .      .  300.0 1100.0      .
 CLEV      .      .  600.0      . 1000.0      . 1000.0
-PITT  900.0 1200.0      .  400.0  400.0      .      .
    +PITT 900.0 1200.0 . 400.0 400.0 . . diff --git a/previews/PR3913/tutorials/nonlinear/classifiers/5248406a.svg b/previews/PR3913/tutorials/nonlinear/classifiers/1713b0a7.svg similarity index 62% rename from previews/PR3913/tutorials/nonlinear/classifiers/5248406a.svg rename to previews/PR3913/tutorials/nonlinear/classifiers/1713b0a7.svg index 38530d897e9..fcd7dc47ab9 100644 --- a/previews/PR3913/tutorials/nonlinear/classifiers/5248406a.svg +++ b/previews/PR3913/tutorials/nonlinear/classifiers/1713b0a7.svg @@ -1,543 +1,543 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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a/previews/PR3913/tutorials/nonlinear/classifiers/94ba83d3.svg +++ b/previews/PR3913/tutorials/nonlinear/classifiers/545de146.svg @@ -1,142 +1,142 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/nonlinear/classifiers/0909b61c.svg b/previews/PR3913/tutorials/nonlinear/classifiers/64f2376e.svg similarity index 63% rename from previews/PR3913/tutorials/nonlinear/classifiers/0909b61c.svg rename to previews/PR3913/tutorials/nonlinear/classifiers/64f2376e.svg index 7432ccdbf94..6ac45df8807 100644 --- a/previews/PR3913/tutorials/nonlinear/classifiers/0909b61c.svg +++ b/previews/PR3913/tutorials/nonlinear/classifiers/64f2376e.svg @@ -1,551 +1,551 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/nonlinear/classifiers/a4133707.svg b/previews/PR3913/tutorials/nonlinear/classifiers/9da9adbb.svg similarity index 62% rename from previews/PR3913/tutorials/nonlinear/classifiers/a4133707.svg rename to previews/PR3913/tutorials/nonlinear/classifiers/9da9adbb.svg index 9bef6967549..39350ca8473 100644 --- a/previews/PR3913/tutorials/nonlinear/classifiers/a4133707.svg +++ b/previews/PR3913/tutorials/nonlinear/classifiers/9da9adbb.svg @@ -1,544 +1,544 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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b/previews/PR3913/tutorials/nonlinear/classifiers/bdfd0cfd.svg similarity index 69% rename from previews/PR3913/tutorials/nonlinear/classifiers/3a0abafd.svg rename to previews/PR3913/tutorials/nonlinear/classifiers/bdfd0cfd.svg index 419de666932..3b4e324bbae 100644 --- a/previews/PR3913/tutorials/nonlinear/classifiers/3a0abafd.svg +++ b/previews/PR3913/tutorials/nonlinear/classifiers/bdfd0cfd.svg @@ -1,20913 +1,20913 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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a/previews/PR3913/tutorials/nonlinear/classifiers/d02cbec6.svg +++ b/previews/PR3913/tutorials/nonlinear/classifiers/f0d80e24.svg @@ -1,1042 +1,1042 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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index c285c3c1f2b..5e15a75a383 100644 --- a/previews/PR3913/tutorials/nonlinear/classifiers/index.html +++ b/previews/PR3913/tutorials/nonlinear/classifiers/index.html @@ -20,9 +20,9 @@ color = :white, size = (600, 600), legend = false, -)Example block output

    We want to split the points into two distinct sets on either side of a dividing line. We'll then label each point depending on which side of the line it happens to fall. Based on the labels of the point, we'll show how to create a classifier using a JuMP model. We can then test how well our classifier reproduces the original labels and the boundary between them.

    Let's make a line to divide the points into two sets by defining a gradient and a constant:

    w_0, g_0 = [5, 3], 8
+)
    Example block output

    We want to split the points into two distinct sets on either side of a dividing line. We'll then label each point depending on which side of the line it happens to fall. Based on the labels of the point, we'll show how to create a classifier using a JuMP model. We can then test how well our classifier reproduces the original labels and the boundary between them.

    Let's make a line to divide the points into two sets by defining a gradient and a constant:

    w_0, g_0 = [5, 3], 8
 line(v::AbstractArray; w = w_0, g = g_0) = w' * v - g
-line(x::Real; w = w_0, g = g_0) = -(w[1] * x - g) / w[2];

    Julia's multiple dispatch feature allows us to define the vector and single-variable form of the line function under the same name.

    Let's add this to the plot:

    Plots.plot!(plot, line; linewidth = 5)
    Example block output

    Now we label the points relative to which side of the line they are. It is numerically useful to have the labels +1 and -1 for the upcoming JuMP formulation.

    labels = ifelse.(line.(eachrow(P)) .>= 0, 1, -1)
+line(x::Real; w = w_0, g = g_0) = -(w[1] * x - g) / w[2];

    Julia's multiple dispatch feature allows us to define the vector and single-variable form of the line function under the same name.

    Let's add this to the plot:

    Plots.plot!(plot, line; linewidth = 5)
    Example block output

    Now we label the points relative to which side of the line they are. It is numerically useful to have the labels +1 and -1 for the upcoming JuMP formulation.

    labels = ifelse.(line.(eachrow(P)) .>= 0, 1, -1)
 Plots.scatter!(
     plot,
     P[:, 1],
@@ -30,7 +30,7 @@
     shape = ifelse.(labels .== 1, :cross, :xcross),
     markercolor = ifelse.(labels .== 1, :blue, :crimson),
     markersize = 8,
-)
    Example block output

    Our goal is to show we can reconstruct the line from just the points and the labels.

    Formulation: linear support vector machine

    A classifier known as the linear support vector machine (SVM) looks for the affine function $L(p) = w^\top p - g$ that satisfies $L(p) < 0$ for all points $p$ with a label -1 and $L(p) \ge 0$ for all points $p$ with a label +1.

    The linearly constrained quadratic program that implements this is:

    \[\begin{aligned} +)Example block output

    Our goal is to show we can reconstruct the line from just the points and the labels.

    Formulation: linear support vector machine

    A classifier known as the linear support vector machine (SVM) looks for the affine function $L(p) = w^\top p - g$ that satisfies $L(p) < 0$ for all points $p$ with a label -1 and $L(p) \ge 0$ for all points $p$ with a label +1.

    The linearly constrained quadratic program that implements this is:

    \[\begin{aligned} \min_{w \in \mathbb{R}^n, \; g \in \mathbb{R}, \; y \in \mathbb{R}^m} \quad & \frac{1}{2} w^\top w + C \; \sum_{i=1}^m y_i \\ \text{subject to } \quad & D \cdot (P w - g) + y \geq \mathbf{1} \\ & y \ge 0. @@ -59,7 +59,7 @@ │ ├ AffExpr in MOI.GreaterThan{Float64}: 100 │ └ VariableRef in MOI.GreaterThan{Float64}: 100 └ Names registered in the model - └ :g, :w, :y, Main.classifier)

    With the solution, we can ask: was the value of the penalty constant "sufficiently large" for this data set? This can be judged in part by the range of the slack variables. If the slack is too large, then we need to increase the penalty constant.

    Let's plot the solution and check how we did:

    Plots.plot!(plot, classifier; linewidth = 5, linestyle = :dashdotdot)
    Example block output

    We find that we have recovered the dividing line from just the information of the points and their labels.

    Nonseparable classes of points

    Now, what if the point sets are not cleanly separable by a line (or a hyperplane in higher dimensions)? Does this still work? Let's repeat the process, but this time we will simulate nonseparable classes of points by intermingling a few nearby points across the previously used line.

    nearby_indices = abs.(line.(eachrow(P))) .< 1.1
+  └ :g, :w, :y, Main.classifier)

    With the solution, we can ask: was the value of the penalty constant "sufficiently large" for this data set? This can be judged in part by the range of the slack variables. If the slack is too large, then we need to increase the penalty constant.

    Let's plot the solution and check how we did:

    Plots.plot!(plot, classifier; linewidth = 5, linestyle = :dashdotdot)
    Example block output

    We find that we have recovered the dividing line from just the information of the points and their labels.

    Nonseparable classes of points

    Now, what if the point sets are not cleanly separable by a line (or a hyperplane in higher dimensions)? Does this still work? Let's repeat the process, but this time we will simulate nonseparable classes of points by intermingling a few nearby points across the previously used line.

    nearby_indices = abs.(line.(eachrow(P))) .< 1.1
 labels_new = ifelse.(nearby_indices, -labels, labels)
 model, classifier = solve_SVM_classifier(P, labels_new)
 plot = Plots.scatter(
@@ -79,7 +79,7 @@
     markercolor = ifelse.(labels_new .== 1, :blue, :crimson),
     markersize = 8,
 )
-Plots.plot!(plot, classifier; linewidth = 5, linestyle = :dashdotdot)
    Example block output

    So our JuMP formulation still produces a classifier, but it mis-classifies some of the nonseparable points.

    We can find out which points are contributing to the shape of the line by looking at the dual values of the affine constraints and comparing them to the penalty constant $C$:

    affine_cons = all_constraints(model, AffExpr, MOI.GreaterThan{Float64})
+Plots.plot!(plot, classifier; linewidth = 5, linestyle = :dashdotdot)
    Example block output

    So our JuMP formulation still produces a classifier, but it mis-classifies some of the nonseparable points.

    We can find out which points are contributing to the shape of the line by looking at the dual values of the affine constraints and comparing them to the penalty constant $C$:

    affine_cons = all_constraints(model, AffExpr, MOI.GreaterThan{Float64})
 active_cons = findall(isapprox.(dual.(affine_cons), C_0; atol = 0.001))
 findall(nearby_indices) ⊆ active_cons
    true

    The last statement tells us that our nonseparable points are actively contributing to how the classifier is defined. The remaining points are of interest and are highlighted:

    P_active = P[setdiff(active_cons, findall(nearby_indices)), :]
 Plots.scatter!(
@@ -89,7 +89,7 @@
     shape = :hexagon,
     markersize = 8,
     markeropacity = 0.5,
-)
    Example block output

    Advanced: duality and the kernel method

    We now consider an alternative formulation for a linear SVM by solving the dual problem.

    The dual program

    The dual of the linear SVM program is also a linearly constrained quadratic program:

    \[\begin{aligned} +)Example block output

    Advanced: duality and the kernel method

    We now consider an alternative formulation for a linear SVM by solving the dual problem.

    The dual program

    The dual of the linear SVM program is also a linearly constrained quadratic program:

    \[\begin{aligned} \min_{u \in \mathbb{R}^m} \quad & \frac{1}{2} u^\top D P P^\top D u - \; \mathbf{1}^\top u \\ \text{subject to } \quad & \mathbf{1}^\top D u = 0 \\ & 0 \leq u \leq C\mathbf{1}. @@ -108,7 +108,7 @@ classifier(x) = line(x; w = w, g = g) return classifier end

    solve_dual_SVM_classifier (generic function with 1 method)

    We recover the line gradient vector $w$ through setting $w = P^\top D u$, and the line constant $g$ as the dual value of the single affine constraint.

    The dual problem has fewer variables and fewer constraints, so in many cases it may be simpler to solve the dual form.

    We can check that the dual form has recovered a classifier:

    classifier = solve_dual_SVM_classifier(P, labels)
-Plots.plot!(plot, classifier; linewidth = 5, linestyle = :dash)
    Example block output

    The kernel method

    Linear SVM techniques are not limited to finding separating hyperplanes in the original space of the dataset. One could first transform the training data under a nonlinear mapping, apply our method, then map the hyperplane back into original space.

    The actual data describing the point set is held in a matrix $P$, but looking at the dual program we see that what actually matters is the Gram matrix $P P^\top$, expressing a pairwise comparison (an inner-product) between each point vector. It follows that any mapping of the point set only needs to be defined at the level of pairwise maps between points. Such maps are known as kernel functions:

    \[k \; : \; \mathbb{R}^n \times \mathbb{R}^n \; \rightarrow \mathbb{R}, \qquad +Plots.plot!(plot, classifier; linewidth = 5, linestyle = :dash)Example block output

    The kernel method

    Linear SVM techniques are not limited to finding separating hyperplanes in the original space of the dataset. One could first transform the training data under a nonlinear mapping, apply our method, then map the hyperplane back into original space.

    The actual data describing the point set is held in a matrix $P$, but looking at the dual program we see that what actually matters is the Gram matrix $P P^\top$, expressing a pairwise comparison (an inner-product) between each point vector. It follows that any mapping of the point set only needs to be defined at the level of pairwise maps between points. Such maps are known as kernel functions:

    \[k \; : \; \mathbb{R}^n \times \mathbb{R}^n \; \rightarrow \mathbb{R}, \qquad (s, t) \mapsto \left< \Phi(s), \Phi(t) \right>\]

    where the right-hand side applies some transformation $\Phi : \mathbb{R}^n \rightarrow \mathbb{R}^{n'}$ followed by an inner-product in that image space.

    In practice, we can avoid having $\Phi$ explicitly given but instead define a kernel function directly between pairs of vectors. This change to using a kernel function without knowing the map is called the kernel method (or sometimes, the kernel trick).

    Classifier using a Gaussian kernel

    We will demonstrate the application of a Gaussian or radial basis function kernel:

    \[k(s, t) = \exp\left( -\mu \lVert s - t \rVert^2_2 \right)\]

    for some positive parameter $\mu$.

    k_gauss(s::Vector, t::Vector; μ = 0.5) = exp(-μ * LinearAlgebra.norm(s - t)^2)
    k_gauss (generic function with 1 method)

    Given a matrix of points expressed row-wise and a kernel, the next function returns the transformed matrix $K$ that replaces $P P^\top$:

    function pairwise_transform(kernel::Function, P::Matrix{T}) where {T}
     m, n = size(P)
     K = zeros(T, m, m)
@@ -151,7 +151,7 @@
     markersize = ifelse.(labels .== 1, 4, 2),
     size = (600, 600),
     legend = false,
-)
    Example block output

    Is the technique capable of generating a distinctly nonlinear surface? Let's solve the Gaussian kernel based quadratic problem with these parameters:

    classifier = solve_kernel_SVM_classifier(k_gauss, B, labels; C = 1e5, μ = 10.0)
+)
    Example block output

    Is the technique capable of generating a distinctly nonlinear surface? Let's solve the Gaussian kernel based quadratic problem with these parameters:

    classifier = solve_kernel_SVM_classifier(k_gauss, B, labels; C = 1e5, μ = 10.0)
 grid = [[x, y] for x in 0:0.01:2, y in 0:0.01:2]
 grid_pos = [Tuple(g) for g in grid if classifier(g) >= 0]
-Plots.scatter!(plot, grid_pos; markersize = 0.2)
    Example block output

    We find that the kernel method can perform well as a nonlinear classifier.

    The result has a fairly strong dependence on the choice of parameters, with larger values of $\mu$ allowing for a more complex boundary while smaller values lead to a smoother boundary for the classifier. Determining a better performing kernel function and choice of parameters is covered by the process of cross-validation with respect to the dataset, where different testing, training and tuning sets are used to validate the best choice of parameters against a statistical measure of error.

    +Plots.scatter!(plot, grid_pos; markersize = 0.2)Example block output

    We find that the kernel method can perform well as a nonlinear classifier.

    The result has a fairly strong dependence on the choice of parameters, with larger values of $\mu$ allowing for a more complex boundary while smaller values lead to a smoother boundary for the classifier. Determining a better performing kernel function and choice of parameters is covered by the process of cross-validation with respect to the dataset, where different testing, training and tuning sets are used to validate the best choice of parameters against a statistical measure of error.

    diff --git a/previews/PR3913/tutorials/nonlinear/complementarity/index.html b/previews/PR3913/tutorials/nonlinear/complementarity/index.html index de2494eff18..ea55322633d 100644 --- a/previews/PR3913/tutorials/nonlinear/complementarity/index.html +++ b/previews/PR3913/tutorials/nonlinear/complementarity/index.html @@ -131,7 +131,7 @@ Objective value : 0.00000e+00 * Work counters - Solve time (sec) : 1.42000e-04 + Solve time (sec) : 1.38000e-04

    An equilibrium solution is to build 389 MW:

    value(x)
    389.31506849315065

    The production in each scenario is:

    value.(Q)
    5-element Vector{Float64}:
  240.0000000000001
  289.9999999999999
@@ -142,4 +142,4 @@
   60.0
   59.99999999999994
   60.68493150684928
- 110.68493150684935
    + 110.68493150684935 diff --git a/previews/PR3913/tutorials/nonlinear/introduction/index.html b/previews/PR3913/tutorials/nonlinear/introduction/index.html index 9986bd6325d..f54cdc32d2f 100644 --- a/previews/PR3913/tutorials/nonlinear/introduction/index.html +++ b/previews/PR3913/tutorials/nonlinear/introduction/index.html @@ -7,4 +7,4 @@ \min_{x \in \mathbb{R}^n} & f_0(x) \\ \;\;\text{s.t.} & l_j \le f_j(x) \le u_j & j = 1 \ldots m \\ & l_i \le x_i \le u_i & i = 1 \ldots n. -\end{align}\]

    Mixed-integer nonlinear linear programs (MINLPs) are extensions of nonlinear programs in which some (or all) of the decision variables take discrete values.

    How to choose a solver

    JuMP supports a range of nonlinear solvers; look for "NLP" in the list of Supported solvers. However, very few solvers support mixed-integer nonlinear linear programs. Solvers supporting discrete variables start with "(MI)" in the list of Supported solvers.

    If the only nonlinearities in your model are quadratic terms (that is, multiplication between two decision variables), you can also use second-order cone solvers, which are indicated by "SOCP." In most cases, these solvers are restricted to convex quadratic problems and will error if you pass a nonconvex quadratic function; however, Gurobi has the ability to solve nonconvex quadratic terms.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    +\end{align}\]

    Mixed-integer nonlinear linear programs (MINLPs) are extensions of nonlinear programs in which some (or all) of the decision variables take discrete values.

    How to choose a solver

    JuMP supports a range of nonlinear solvers; look for "NLP" in the list of Supported solvers. However, very few solvers support mixed-integer nonlinear linear programs. Solvers supporting discrete variables start with "(MI)" in the list of Supported solvers.

    If the only nonlinearities in your model are quadratic terms (that is, multiplication between two decision variables), you can also use second-order cone solvers, which are indicated by "SOCP." In most cases, these solvers are restricted to convex quadratic problems and will error if you pass a nonconvex quadratic function; however, Gurobi has the ability to solve nonconvex quadratic terms.

    How these tutorials are structured

    Having a high-level overview of how this part of the documentation is structured will help you know where to look for certain things.

    diff --git a/previews/PR3913/tutorials/nonlinear/nested_problems/index.html b/previews/PR3913/tutorials/nonlinear/nested_problems/index.html index 2bec6f6ca53..cd88f0d73a0 100644 --- a/previews/PR3913/tutorials/nonlinear/nested_problems/index.html +++ b/previews/PR3913/tutorials/nonlinear/nested_problems/index.html @@ -64,7 +64,7 @@ Dual objective value : 0.00000e+00 * Work counters - Solve time (sec) : 4.87575e-01 + Solve time (sec) : 4.78782e-01 Barrier iterations : 32

    The optimal objective value is:

    objective_value(model)
    -418983.48680640775

    and the optimal upper-level decision variables $x$ are:

    value.(x)
    2-element Vector{Float64}:
  154.97862337234338
@@ -127,8 +127,8 @@
   Dual objective value : 0.00000e+00
 
 * Work counters
-  Solve time (sec)   : 1.90832e-01
+  Solve time (sec)   : 1.85007e-01
   Barrier iterations : 32

    an we can check we get the same objective value:

    objective_value(model)
    -418983.48680640775

    and upper-level decision variable $x$:

    value.(x)
    2-element Vector{Float64}:
  154.97862337234338
- 180.0096143098799
    + 180.0096143098799 diff --git a/previews/PR3913/tutorials/nonlinear/operator_ad/index.html b/previews/PR3913/tutorials/nonlinear/operator_ad/index.html index bec561e3ae8..8b98116ac69 100644 --- a/previews/PR3913/tutorials/nonlinear/operator_ad/index.html +++ b/previews/PR3913/tutorials/nonlinear/operator_ad/index.html @@ -205,4 +205,4 @@ di_rosenbrock(; backend = DifferentiationInterface.AutoForwardDiff())
    2-element Vector{Float64}:
  0.9999999999999899
- 0.9999999999999792
    + 0.9999999999999792 diff --git a/previews/PR3913/tutorials/nonlinear/portfolio/fae64cdb.svg b/previews/PR3913/tutorials/nonlinear/portfolio/4709c5c7.svg similarity index 79% rename from previews/PR3913/tutorials/nonlinear/portfolio/fae64cdb.svg rename to previews/PR3913/tutorials/nonlinear/portfolio/4709c5c7.svg index 89fa27d9539..7a26df13511 100644 --- a/previews/PR3913/tutorials/nonlinear/portfolio/fae64cdb.svg +++ b/previews/PR3913/tutorials/nonlinear/portfolio/4709c5c7.svg @@ -1,581 +1,581 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/nonlinear/portfolio/index.html b/previews/PR3913/tutorials/nonlinear/portfolio/index.html index b48165b78b3..49be25ae1ff 100644 --- a/previews/PR3913/tutorials/nonlinear/portfolio/index.html +++ b/previews/PR3913/tutorials/nonlinear/portfolio/index.html @@ -72,7 +72,7 @@ Dual objective value : 4.52688e+04 * Work counters - Solve time (sec) : 3.05986e-03 + Solve time (sec) : 2.97499e-03 Barrier iterations : 11

    The optimal allocation of our assets is:

    value.(x)
    3-element Vector{Float64}:
  497.045529849864
@@ -103,7 +103,7 @@
   Objective bound    : [5.78303e-09,-7.37159e+01]
 
 * Work counters
-  Solve time (sec)   : 2.26454e-01
+  Solve time (sec)   : 2.22103e-01

    The algorithm found 50 different solutions. Let's plot them to see how they differ:

    objective_space = Plots.hline(
     [scalar_return];
     label = "Single-objective solution",
@@ -135,4 +135,4 @@
     ylabel = "Investment (\$)",
     title = "Decision space",
 )
-Plots.plot(objective_space, decision_space; layout = (2, 1), size = (600, 600))
    Example block output

    Perhaps our trade-off wasn't so bad after all. Our original solution corresponded to picking a solution #17. If we buy more SEHI, we can increase the return, but the variance also increases. If we buy less SEHI, such as a solution like #5 or #6, then we can achieve the corresponding return without deploying all of our capital. We should also note that at no point should we buy WMT.

    +Plots.plot(objective_space, decision_space; layout = (2, 1), size = (600, 600))Example block output

    Perhaps our trade-off wasn't so bad after all. Our original solution corresponded to picking a solution #17. If we buy more SEHI, we can increase the return, but the variance also increases. If we buy less SEHI, such as a solution like #5 or #6, then we can achieve the corresponding return without deploying all of our capital. We should also note that at no point should we buy WMT.

    diff --git a/previews/PR3913/tutorials/nonlinear/querying_hessians/index.html b/previews/PR3913/tutorials/nonlinear/querying_hessians/index.html index 2843d5be48d..033efe21d10 100644 --- a/previews/PR3913/tutorials/nonlinear/querying_hessians/index.html +++ b/previews/PR3913/tutorials/nonlinear/querying_hessians/index.html @@ -168,4 +168,4 @@ 2.82843 2.82843

    Compare that to the analytic solution:

    y = value.(x)
 [2y[1] 0; 2y[1]+2y[2] 2y[1]+2y[2]]
    2×2 Matrix{Float64}:
  1.58072  0.0
- 2.82843  2.82843
    + 2.82843 2.82843 diff --git a/previews/PR3913/tutorials/nonlinear/rocket_control/cd2597b6.svg b/previews/PR3913/tutorials/nonlinear/rocket_control/e9a339cb.svg similarity index 89% rename from previews/PR3913/tutorials/nonlinear/rocket_control/cd2597b6.svg rename to previews/PR3913/tutorials/nonlinear/rocket_control/e9a339cb.svg index b2692748428..609c7d6e9b7 100644 --- a/previews/PR3913/tutorials/nonlinear/rocket_control/cd2597b6.svg +++ b/previews/PR3913/tutorials/nonlinear/rocket_control/e9a339cb.svg @@ -1,130 +1,130 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/nonlinear/rocket_control/index.html b/previews/PR3913/tutorials/nonlinear/rocket_control/index.html index 3a5e7553376..a62314e4b2f 100644 --- a/previews/PR3913/tutorials/nonlinear/rocket_control/index.html +++ b/previews/PR3913/tutorials/nonlinear/rocket_control/index.html @@ -48,7 +48,7 @@ Dual objective value : 4.66547e+00 * Work counters - Solve time (sec) : 1.53621e-01 + Solve time (sec) : 1.53069e-01 Barrier iterations : 24

    Finally, we plot the solution:

    function plot_trajectory(y; kwargs...)
     return Plots.plot(
@@ -66,4 +66,4 @@
     plot_trajectory(x_v; ylabel = "Velocity"),
     plot_trajectory(u_t; ylabel = "Thrust");
     layout = (2, 2),
-)
    Example block output

    Next steps

    • Experiment with different values for the constants. How does the solution change? In particular, what happens if you change T_max?
    • The dynamical equations use rectangular integration for the right-hand side terms. Modify the equations to use the Trapezoidal rule instead. (As an example, x_v[t-1] would become 0.5 * (x_v[t-1] + x_v[t]).) Is there a difference?
    +)Example block output

    Next steps

    • Experiment with different values for the constants. How does the solution change? In particular, what happens if you change T_max?
    • The dynamical equations use rectangular integration for the right-hand side terms. Modify the equations to use the Trapezoidal rule instead. (As an example, x_v[t-1] would become 0.5 * (x_v[t-1] + x_v[t]).) Is there a difference?
    diff --git a/previews/PR3913/tutorials/nonlinear/simple_examples/index.html b/previews/PR3913/tutorials/nonlinear/simple_examples/index.html index 92bc1298a19..691801a2a94 100644 --- a/previews/PR3913/tutorials/nonlinear/simple_examples/index.html +++ b/previews/PR3913/tutorials/nonlinear/simple_examples/index.html @@ -181,4 +181,4 @@ z ≥ 0 Objective value: 0.32699283491387243 x = 0.32699283491387243 -y = 0.2570658388068964 +y = 0.2570658388068964 diff --git a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/e676b1de.svg b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/9924f312.svg similarity index 88% rename from previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/e676b1de.svg rename to previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/9924f312.svg index fb73e051a7e..130da739aad 100644 --- a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/e676b1de.svg +++ b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/9924f312.svg @@ -1,182 +1,182 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/86e291c1.svg b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/c6d6fc0e.svg similarity index 88% rename from previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/86e291c1.svg rename to previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/c6d6fc0e.svg index 159a6bd00fa..567b3e7a6d3 100644 --- a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/86e291c1.svg +++ b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/c6d6fc0e.svg @@ -1,97 +1,97 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + - + - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/71af12c5.svg b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/dd4a8967.svg similarity index 87% rename from previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/71af12c5.svg rename to previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/dd4a8967.svg index aca03de1872..2c4be72346d 100644 --- a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/71af12c5.svg +++ b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/dd4a8967.svg @@ -1,48 +1,48 @@ - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/index.html b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/index.html index 16880a92704..c8270072fdf 100644 --- a/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/index.html +++ b/previews/PR3913/tutorials/nonlinear/space_shuttle_reentry_trajectory/index.html @@ -221,7 +221,7 @@ layout = grid(3, 2), linewidth = 2, size = (700, 700), -)Example block output
    function q(h, v, a)
+)
    Example block output
    function q(h, v, a)
     ρ(h) = ρ₀ * exp(-h / hᵣ)
     qᵣ(h, v) = 17700 * √ρ(h) * (0.0001 * v)^3.07
     qₐ(a) = c₀ + c₁ * rad2deg(a) + c₂ * rad2deg(a)^2 + c₃ * rad2deg(a)^3
@@ -255,7 +255,7 @@
     layout = grid(3, 1),
     linewidth = 2,
     size = (700, 700),
-)
    Example block output
    plot(
+)
    Example block output
    plot(
     rad2deg.(value.(ϕ)),
     rad2deg.(value.(θ)),
     value.(scaled_h);
@@ -265,4 +265,4 @@
     xlabel = "Longitude (deg)",
     ylabel = "Latitude (deg)",
     zlabel = "Altitude (100,000 ft)",
-)
    Example block output +)Example block output diff --git a/previews/PR3913/tutorials/nonlinear/tips_and_tricks/index.html b/previews/PR3913/tutorials/nonlinear/tips_and_tricks/index.html index 1b8d08d2be8..8802d865f8a 100644 --- a/previews/PR3913/tutorials/nonlinear/tips_and_tricks/index.html +++ b/previews/PR3913/tutorials/nonlinear/tips_and_tricks/index.html @@ -69,4 +69,4 @@ @assert is_solved_and_feasible(model) Test.@test objective_value(model) ≈ √3 atol = 1e-4 Test.@test value.(x) ≈ [1.0, 1.0] atol = 1e-4 -println("Memoized approach: function_calls = $(function_calls)")
    Memoized approach: function_calls = 22

    Compared to the naive approach, the memoized approach requires half as many function evaluations.

    +println("Memoized approach: function_calls = $(function_calls)")
    Memoized approach: function_calls = 22

    Compared to the naive approach, the memoized approach requires half as many function evaluations.

    diff --git a/previews/PR3913/tutorials/nonlinear/user_defined_hessians/index.html b/previews/PR3913/tutorials/nonlinear/user_defined_hessians/index.html index 3599113340d..e1f45703561 100644 --- a/previews/PR3913/tutorials/nonlinear/user_defined_hessians/index.html +++ b/previews/PR3913/tutorials/nonlinear/user_defined_hessians/index.html @@ -39,6 +39,6 @@ Dual solution : * Work counters - Solve time (sec) : 3.57661e-02 + Solve time (sec) : 3.75781e-02 Barrier iterations : 14 - + diff --git a/previews/PR3913/tutorials/transitioning/transitioning_from_matlab/index.html b/previews/PR3913/tutorials/transitioning/transitioning_from_matlab/index.html index 2860007a199..239915732cd 100644 --- a/previews/PR3913/tutorials/transitioning/transitioning_from_matlab/index.html +++ b/previews/PR3913/tutorials/transitioning/transitioning_from_matlab/index.html @@ -58,7 +58,7 @@ 6 1.1746e-09 -1.2507e-09 2.43e-09 1.59e-16 6.59e-17 2.83e-10 3.87e-10 9.90e-01 --------------------------------------------------------------------------------------------- Terminated with status = solved -solve time = 897μs

    The exclamation mark here is a Julia-ism that means the function is modifying its argument, model.

    Querying solution status

    After the optimization is done, you should check for the solution status to see what solution (if any) the solver found.

    Like YALMIP and CVX, JuMP provides a solver-independent way to check it, via the command:

    is_solved_and_feasible(model)
    true

    If the return value is false, you should investigate with termination_status, primal_status, and raw_status, See Solutions for more details on how to query and interpret solution statuses.

    Extracting variables

    Like YALMIP, but unlike CVX, with JuMP you need to explicitly ask for the value of your variables after optimization is done, with the function call value(x) to obtain the value of variable x.

    value.(m[1][1, 1])
    0.0

    A subtlety is that, unlike YALMIP, the function value is only defined for scalars. For vectors and matrices you need to use Julia broadcasting: value.(v).

    value.(m[1])
    3×3 Matrix{Float64}:
+solve time =  649μs

    The exclamation mark here is a Julia-ism that means the function is modifying its argument, model.

    Querying solution status

    After the optimization is done, you should check for the solution status to see what solution (if any) the solver found.

    Like YALMIP and CVX, JuMP provides a solver-independent way to check it, via the command:

    is_solved_and_feasible(model)
    true

    If the return value is false, you should investigate with termination_status, primal_status, and raw_status, See Solutions for more details on how to query and interpret solution statuses.

    Extracting variables

    Like YALMIP, but unlike CVX, with JuMP you need to explicitly ask for the value of your variables after optimization is done, with the function call value(x) to obtain the value of variable x.

    value.(m[1][1, 1])
    0.0

    A subtlety is that, unlike YALMIP, the function value is only defined for scalars. For vectors and matrices you need to use Julia broadcasting: value.(v).

    value.(m[1])
    3×3 Matrix{Float64}:
  0.0  0.0  0.0
  0.0  0.0  0.0
  0.0  0.0  0.0

    There is also a specialized function for extracting the value of the objective, objective_value(model), which is useful if your objective doesn't have a convenient expression.

    objective_value(model)
    -5.999999998825352

    Dual variables

    Like YALMIP and CVX, JuMP allows you to recover the dual variables. In order to do that, the simplest method is to name the constraint you're interested in, for example, @constraint(model, bob, sum(v) == 1) and then, after the optimzation is done, call dual(bob). See Duality for more details.

    Reformulating problems

    Perhaps the biggest difference between JuMP and YALMIP and CVX is how far the package is willing to go in reformulating the problems you give to it.

    CVX is happy to reformulate anything it can, even using approximations if your solver cannot handle the problem.

    YALMIP will only do exact reformulations, but is still fairly adventurous, for example, being willing to reformulate a nonlinear objective in terms of conic constraints.

    JuMP does no such thing: it only reformulates objectives into objectives, and constraints into constraints, and is fairly conservative at that. As a result, you might need to do some reformulations manually, for which a good guide is the Modeling with cones tutorial.

    Vectorization

    In MATLAB, it is absolutely essential to "vectorize" your code to obtain acceptable performance. This is because MATLAB is a slow interpreted language, which sends your commands to fast libraries. When you "vectorize" your code you are minimizing the MATLAB part of the work and sending it to the fast libraries instead.

    There's no such duality with Julia.

    Everything you write and most libraries you use will compile down to LLVM, so "vectorization" has no effect.

    For example, if you are writing a linear program in MATLAB and instead of the usual constraints = [v >= 0] you write:

    for i = 1:n
@@ -157,4 +157,4 @@
     x = randn(d, 1) + 1i * randn(d, 1);
     y = x * x';
     rho = y / trace(y);
-end
    +end