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gencan.f
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gencan.f
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c
c Written by Ernesto G. Birgin, 2009-2011.
c Copyright (c) 2009-2011, Jose Mario Martinez,
c Ernesto G. Birgin.
c
c This program is free software; you can redistribute it and/or
c modify it under the terms of the GNU General Public License
c as published by the Free Software Foundation; either version 2
c of the License, or (at your option) any later version.
c
c
c Subroutine pgencan: This is only a interface to set some
c parameters that we do not change in packmol.
c
subroutine pgencan(n,x,fx)
implicit none
include 'sizes.i'
include 'molpa.i'
include 'gencan.i'
double precision l(nn), lambda(1), rho(1), u(nn), wd(8*nn)
double precision epsgpsn,gpsupn,delmin
double precision x(nn), fx, g(nn)
integer m,iprint,maxfc,ncomp,iter,fcnt,gcnt,cgcnt,inform
integer wi(nn)
integer n, i
integer trtype1
m = 0
do i = 1,n
l(i) = - 1.0d+20
u(i) = 1.0d+20
end do
epsgpsn = 1.0d-06
maxfc = 10 * maxit
if(init1) iprint = iprint1
if(.not.init1) iprint = iprint2
ncomp = 50
delmin = 2.d0
trtype1 = 1
call easygencan(n,x,l,u,m,lambda,rho,epsgpsn,maxit,maxfc,
+ trtype1,iprint,ncomp,fx,g,gpsupn,iter,fcnt,
+ gcnt,cgcnt,inform,wi,wd,delmin)
if( inform.ne.7 .and.
+ (iprint1.gt.0 .or. iprint2.gt.0) ) write(*,*)
return
end
C *****************************************************************
C *****************************************************************
subroutine evalal(n,x,m,lambda,rho,f,flag)
C This subroutine computes the objective function when GENCAN is
C being used stand-alone to solve a unique bound-constrained problem.
C When GENCAN is being used in an Augmented Lagrangian framework,
C this subroutine must compute the Augmented Lagrangian function.
C
C On Entry:
C
C n integer,
C number of variables,
C
C x double precision x(n),
C current point,
C
C m integer,
C number of constraints (equalities plus inequalities),
C
C lambda double precision lambdae(m),
C current estimation of the Lagrange multipliers,
C
C rho double precision rho(m)
C penalty parameters,
C
C NOTE: arguments m, lambda and rho are useful when GENCAN is being used
C for solving the box-constrained subproblems of an Augmented Lagrangian
C framework. When GENCAN is being used stand-alone for solving a bound-
C constrained problem, these arguments are dummy arguments.
C
C On Return
C
C f double precision,
C objective function value at x,
C
C flag integer
C 0 means "no errors",
C 1 means "some error occurs in the objective funtion evaluation".
implicit none
C SCALAR ARGUMENTS
integer flag,m,n
double precision f
C ARRAY ARGUMENTS
double precision lambda(m),rho(m),x(n)
C LOCAL SCALARS
flag = 0
call feasy(x,f)
end
C *****************************************************************
C *****************************************************************
subroutine evalnal(n,x,m,lambda,rho,g,flag)
C This subroutine computes the gradient of the objective function
C when GENCAN is being used stand-alone to solve a unique bound-
C constrained problem. When GENCAN is being used in an Augmented
C Lagrangian framework, this subroutine must compute the gradient of
C Augmented Lagrangian.
C
C On Entry:
C
C n integer,
C number of variables,
C
C x double precision x(n),
C current point,
C
C m integer,
C number of constraints (equalities plus inequalities),
C
C lambda double precision lambdae(m),
C current estimation of the Lagrange multipliers,
C
C rho double precision rho(m)
C penalty parameters,
C
C NOTE: arguments m, lambda and rho are useful when GENCAN is being used
C for solving the box-constrained subproblems of an Augmented Lagrangian
C framework. When GENCAN is being used stand-alone for solving a bound-
C constrained problem, these arguments are dummy arguments.
C
C On Return
C
C g double precision g(n),
C gradient of the objective function at x,
C
C flag integer
C 0 means "no errors",
C 1 means "some error occurs in the gradient evaluation".
implicit none
C SCALAR ARGUMENTS
integer flag,m,n
C ARRAY ARGUMENTS
double precision g(n),lambda(m),rho(m),x(n)
C LOCAL SCALARS
flag = 0
call geasy(n,x,g)
end
C *****************************************************************
C *****************************************************************
c Modified by L. Martinez (there was an error on the number of
c parameters when calling this subroutine). This subroutine does
c nothing.
c subroutine evalhd(nind,ind,n,x,m,lambda,rho,d,hd,flag)
subroutine evalhd(n)
C This subroutine computes the product of the Hessian matrix times
C the input vector argument d. If GENCAN is being used stand-alone
C to solve a bound-constrained problem, the ''Hessian matrix'' must
C be the Hessian matrix of the objective function. On the other hand,
C if GENCAN is being used to solve the bound-constrained subproblems
C in an Augmented Lagrangian framework, the Hessian matrix must be
C the Hessian of the Augmented Lagrangian function.
C
C IMPORTANT: This subroutine does not need to be coded if the user
C prefers to approximate the Hessian-vector product by incremental
C quotients. In this case, it is enough to set the GENCAN input
C argument htvtype equal to 1 and an internal GENCAN subroutine will
C be used to compute the approximation. In fact, this is the default
C GENCAN option. See the GENCAN and EASYGENCAN arguments descriptions
C for details.
C
C On Entry:
C
C nind integer
C number of component of the Hessian-vector product that
C must be computed,
C
C ind integer ind(nind)
C the component that must be computed are ind(1)-th ... ind(nind)-th,
C
C n integer,
C number of variables,
C
C x double precision x(n),
C current point,
C
C m integer,
C number of constraints (equalities plus inequalities),
C
C lambda double precision lambdae(m),
C current estimation of the Lagrange multipliers,
C
C rho double precision rho(m)
C penalty parameters,
C
C d double precision d(n)
C vector of the Hessian-vector product.
C
C NOTE: arguments m, lambda and rho are useful when GENCAN is being used
C for solving the box-constrained subproblems of an Augmented Lagrangian
C framework. When GENCAN is being used stand-alone for solving a bound-
C constrained problem, these arguments are dummy arguments.
C
C On Return
C
C hd double precision g(n),
C Hessian-vector product,
C
C flag integer
C 0 means "no errors",
C 1 means "some error occurs in the gradient evaluation".
implicit none
C SCALAR ARGUMENTS
c integer flag,m,n,nind
integer n
C ARRAY ARGUMENTS
c integer ind(nind)
c double precision d(n),hd(n),lambda(m),rho(m),x(n)
c flag = - 1
end
C**************************************************************************
C Last update of EASYGENCAN: February 18th, 2005.
subroutine easygencan(n,x,l,u,m,lambda,rho,epsgpsn,maxit,maxfc,
+trtype,iprint,ncomp,f,g,gpsupn,iter,fcnt,gcnt,cgcnt,inform,wi,wd,
+delmin)
implicit none
C SCALAR ARGUMENTS
integer cgcnt,fcnt,gcnt,m,maxfc,maxit,n,ncomp,inform,iprint,iter
double precision epsgpsn,f,gpsupn
C ARRAY ARGUMENTS
integer wi(n)
double precision g(n),l(n),lambda(m),rho(m),u(n),wd(8*n),x(n)
C This subroutine aims to simplify the use of GENCAN. For this
C purpose it gives values to most of the GENCAN arguments and
C leaves to the user those arguments which he/she may would like to
C set by him/herself.
C
C The arguments of EASYGENCAN are the input and output arguments of
C GENCAN that are supposed to be useful for a common user. The input
C arguments are mostly related to basic problem information, like
C dimension and bounds, and the initial point. There are also input
C arguments related to simple stopping criteria (like norm of the
C projected gradient, and maximum number of iterations and
C functional evaluations). There are also two input arguments
C related to control the amount of information written into the
C screen. The output arguments are related to information of the
C solution and some few performance measurements. Basically, on
C return, EASYGENCAN gives to the user the solution, the objective
C functional value and its gradient at the solution, Euclidian and
C sup-norm of the projected gradient at the solution, the number of
C iterations, functional and gradient evaluations, and Conjugate
C Gradient iterations used to reach the solution, and, finally, a
C flag that indicates the stopping criterion that was satisfied.
C
C All the other arguments of GENCAN are setted with its default
C values by EASYGENCAN. EASYGENCAN divides the arguments of GENCAN
C in two sets. Those that are related to the behaviour of GENCAN are
C declared as Fortran parameters (constants). The other arguments of
C GENCAN, most of them related to alternative stopping criteria, and
C that may depend of, for example, maxit, are declared as local
C variables of EASYGENCAN.
C
C GENCAN arguments that are defined as Fortran parameters in this
C subroutine are GENCAN arguments that should not be modified by a
C common user. They are arguments that modify the behaviour of
C GENCAN and whos values were selected because they are classical
C values in some cases or because some numerical experiments seemed
C to indicate that they are the best choices.
C
C GENCAN arguments that are declared as local variables in this
C subroutine are GENCAN arguments that may be modified if, with
C their suggested values, GENCAN does not give the desired result.
C Most of them are related to Conjugate Gradients or to disabled
C stopping criteria that may be useful in bad-scaled problems or
C problems with not trustable derivatives.
C
C Finally, this subroutine declares as local variables some
C arguments of GENCAN which in fact are output arguments. Most of
C them are related to quantities that can be used for statistics
C related to the GENCAN performance, like number Spectral Projected
C Gradient iterations, Truncated Newton iterations, Conjugate
C Gradient iterations, etc. As we assume that this values are not
C useful for the common user, this subroutine throw all of them
C away.
C
C We describe below the meaning of the arguments of the EASYGENCAN
C subroutine. More detailed descriptions as well as the descriptions
C of all the other GENCAN arguments that are not arguments of
C EASYGENCAN are also described at the begining of the GENCAN
C subroutine.
C
C On entry:
C
C n integer
C number of variables
C
C x double precision x(n)
C initial estimation of the solution
C
C l double precision l(n)
C lower bounds on the variables
C
C u double precision u(n)
C upper bounds on the variables
C
C m integer
C lambda double precision lambda(m)
C rho double precision rho(m)
C These three parameters are not used nor modified by
C GENCAN and they are passed as arguments to the user-
C defined subroutines evalal and evalnal to compute the
C objective function and its gradient, respectively.
C Clearly, in an Augmented Lagrangian context, if GENCAN is
C being used to solve the bound-constrainted subproblems, m
C would be the number of constraints, lambda the Lagrange
C multipliers approximation and rho the penalty parameters
C
C epsgpsn double precision
C GENCAN stops declaring convergence if it finds a point
C whos projected gradient sup-norm is smaller than or equal
C to epsgpsn
C
C maxit integer
C GENCAN stops declaring ''maximum number of iteration
C achieved'' if the number of iterations exceeds maxit
C
C maxfc integer
C the same as before but with the number of functional
C evaluations
C
C iprint integer
C indicates the degree of details of the output generated
C by GENCAN. Setting iprint to a value smaller than 2 will
C make GENCAN to generate no output at all. An iprint value
C greater than or equal to 2 will generate information of
C every GENCAN iteration. An iprint value greater than or
C equal to 3 will also show information of the Conjugate
C Gradient iterations (used to compute the Truncated Newton
C direction) and also information related to the line
C search procedures in the Spectral Projected Gradient
C direction and the Truncated Newton direction.
C
C ncomp integer
C Sometimes, vectors like the current point x, the gradient
C of the objective function g, or the search directions
C (Spectral Projected Gradient direction or Truncated
C Newton direction), among other vector, are showed in the
C screen. In such cases, if the problem dimension is large,
C to show just a few elements of these vectors may be
C preferable. Argument ncomp can be used to indicate how
C many array elements must be displayed.
C
C wi integer wi(n)
C integer working space
C
C wd double precision wd(8*n)
C double precision working space
C
C On return:
C
C x double precision x(n)
C estimation of the solution
C
C f double precision
C objective function value at the solution
C
C g double precision g(n)
C gradient of the objective function at the solution
C
C gpsupn double precision
C sup-norm of the continuous projected gradient
C
C iter integer
C number of iterations used to reach the solution
C
C fcnt integer
C number of functional evaluations
C
C gcnt integer
C number of gradient evaluations
C
C cgcnt integer
C number of Conjugate Gradient iterations
C
C inform integer
C termination criteria. inform equal to 1 means that
C GENCAN converged with the sup-norm of the continuous
C projected gradient stopping criterion (inform equal to 0
C means the same but with the Euclidian norm). Other
C positive values means that GENCAN stopped by a may be not
C successful stopping criteria. A negative value means that
C there was an error in the user-defined subroutines that
C computes the objective function (subroutine evalal), the
C gradient (subroutine evalnal), or the Hessian-vector
C product (subroutine evalhd). See the GENCAN description
C for more details.
C HERE STARTS THE DESCRIPTION OF SOME GENCAN ARGUMENTS THAT ARE
C BEING SETTED INSIDE EASYGENCAN. THE FIRST SET OF ARGUMENTS ARE
C THOSE ARGUMENTS THAT WE WILL CALL ''CONSTANTS'' AND THAT, AS THEIR
C VALUES ALTER THE BEHAVIOUR OF GENCAN, SHOULD NOT BE MODIFIED BY A
C COMMON USER.
C CONSTANTS FOR GENERAL USES
C Steps: h = max( steabs, sterel * abs( x ) ) should be a number
C such that h is small ( relatively to x ) and x + h is different
C from x. So, h is something that can be used a a step for a finite
C differences approximation of a partial derivative relative to x.
C Epsilons: something smaller than max( epsabs, epsrel * abs( x ) )
C should be considered as ``zero'' when compared with x. It is used,
C for example, to detect that a step taken during a line search is
C too small.
C Infinitys: infrel is a big number that may appear in the
C calculations. infabs is a number that should never be reached in
C the calculations and is used the represent ``infinite''. Detailed
C explanations of how are they used are rather cumbersome.
double precision steabs,sterel,epsabs,epsrel,infabs,infrel
parameter ( steabs = 1.0d-10 )
parameter ( sterel = 1.0d-07 )
parameter ( epsabs = 1.0d-20 )
parameter ( epsrel = 1.0d-10 )
parameter ( infabs = 1.0d+99 )
parameter ( infrel = 1.0d+20 )
C CONSTANTS FOR CLASSICAL LINE-SEARCH CONDITIONS
C beta is the constant for the ''beta condition''. We use this
C condition to test whether is promising to extrapolate or not.
C gamma is the constant for the sufficient decrease ''Armijo
C condition''.
C theta is the constant for the ''angle condition''.
C sigma1 and sigma2 are the constants for the safeguarding quadratic
C interpolations. We use them in a rather unusual way. Instead of
C discarding a new step anew if it does not belong to the interval
C [ sigma1 * aprev, sigma2 * aprev ], we discard it if it does not
C belong to the interval [ sigma1, sigma2 * aprev ]. In such a case
C we take something similar to ''anew = aprev / 2''.
double precision beta,gamma,theta,sigma1,sigma2
parameter ( beta = 0.5d0 )
parameter ( gamma = 1.0d-04 )
parameter ( theta = 1.0d-06 )
parameter ( sigma1 = 0.1d0 )
parameter ( sigma2 = 0.9d0 )
C CONSTANTS FOR SPECIFIC PROCEDURES (NOT SO CLASSICAL)
C In line searches, when interpolating, the step may become so
C small that we should declare a line search failure indicating that
C direction may not be a descent direction. This decision is never
C take before doing at least mininterp interpolations.
C In line searches, the beta condition (see above) may recommend to
C extrapolate. We never do more than maxextrap extrapolations.
C In the line searches, when we need to interpolate and the result
C of the quadratic interpolation is rejected, the new step is
C computed as anew = aprev / nint. When the beta condition
C recommends to extrapolate, we compute anew = aprev * next.
C When computing the Newton direction by Conjugate Gradients we
C never go further an artificial ''trust region''. This ''trust
C radius'' is never smaller than delmin.
C In active set strategies, constants eta is used to decide whether
C the current face should be abandoned or not. In particular, the
C current face is abandoned when the norm of the internal to face
C component of the continuous projected gradient is smaller than
C ( 1 - eta ) times the norm of the continuous projected gradient.
C In this way, values of eta near 1 makes the method to work hard
C inside the faces and values of eta near 0 makes the method to
C abandon the faces very quickly.
C We always use as a first step in a line search procedure along a
C first order direction the spectral steplength. This steplength
C must belong to the interval [lspgmi,lspgma].
integer maxextrap,mininterp
parameter ( maxextrap = 100 )
parameter ( mininterp = 4 )
double precision nint,next,delmin,eta,lspgma,lspgmi
parameter ( nint = 2.0d0 )
parameter ( next = 2.0d0 )
c parameter ( delmin = 1.d4 )
parameter ( eta = 0.9d0 )
parameter ( lspgma = 1.0d+10 )
parameter ( lspgmi = 1.0d-10 )
C DIMENSIONS FOR SOME WORKING SPACES
C In non-monotone line searches, given p, the last p objective
C functional values must be stored. For this reason we declare a
C vector with pmax double precision elements. So p must be less than
C or equal to pmax.
C Sometimes, is the problem is bad scaled, to request a small
C gradient norm at the solution may be inadequate. For this reason,
C a test to verify if this norm is not decreasing during maxitngp
C (MAXimum of ITerations with No Gradient Progress) consecutive
C iterations then we stop the method with a warning. As it is not
C expected a monotone decreasing of the gradient norm, again, the
C norm of the last maxitngp iterations must be saved. For this
C purpose, we declare a vector of tmax elements. So maxitngp must
C be less than or equal to tmax.
integer tmax
parameter ( tmax = 10000 )
C HERE STARTS THE DESCRIPTION OF THE OTHER ARGUMENTS OF GENCAN BEING
C SETTED BY EASYGENCAN. THESE ARGUMENTS MAY BE MODIFIED BY A COMMON
C USER IF, WITH THEIR SUGGESTED VALUES, GENCAN DOES NOT GIVE THE
C EXPECTED RESULT.
C GENCAN INPUT ARGUMENTS THAT WILL BE SETTED BELOW
logical nearlyq
integer cgmaxit,cgscre,gtype,htvtype,maxitnfp,maxitngp,maxitnqmp,
+ trtype
double precision cgepsf,cgepsi,cggpnf,delta0,epsgpen,epsnfp,
+ epsnqmp,fmin
C GENCAN OUTPUT ARGUMENTS THAT WILL BE DISCARDED
integer spgfcnt,spgiter,tnexbcnt,tnexgcnt,tnexbfe,tnexgfe,tnfcnt,
+ tnintcnt,tnintfe,tniter,tnstpcnt
double precision gpeucn2
C GENCAN WORKING VECTORS (WHICH DIMENSION IS NOT RELATED TO THE
C PROBLEM DIMENSION)
double precision lastgpns(tmax)
C ARGUMENTS RELATED TO DERIVATIVES CALCULATIONS
C gtype indicates in which way the gradient of the objective
C function will be computed. If the user have been implemented the
C user-supplied evalnal subroutine to compute the gradient of the
C objective function then gtype argument must be set to 0 (ZERO) and
C the user-supplied evalnal subroutine will be called by GENCAN any
C time the gradient would be required.
C
C The prototype of the evalnal subroutine must be:
C
C subroutine evalnal(n,x,m,lambda,rho,nal,flag)
C
C SCALAR ARGUMENTS
C integer n,m,flag
C
C ARRAY ARGUMENTS
C double precision x(n),lambda(m),rho(m),nal(n)
C
C ''Here must be written the subroutine body that calculates the
C n-dimensional gradient vector of the objective function
C evaluated at x and saves it in nal. It also must set flag to 0
C (ZERO) if the gradient was successfully computed and to any
C other value if the gradient vector is not well defined at the
C required point x. If GENCAN is been used stand-alone to solve
C a unique bound-constrained problem then m, lambda and rho are
C dummy arguments. On the other hand, if GENCAN is been used in
C an Augmented Lagrangian framework then these arguments should
C be used for the number of constraints, the Lagrange
C multipliers approximation and the penalty parameters,
C respectively.''
C
C end
C
C If, on the other hand, the user is not able to provide evalnal
C subroutine, gtype argument must be set to 1 (ONE). In this case,
C every time GENCAN needs to compute the gradient of the objective
C function, an internal subroutine that approximates it by finite-
C differences will be used (be aware that it maybe very time
C consuming). Moreover, note that the evalnal subroutine must still
C be present (with an empty body).
gtype = 0
C htvtype indicates in which way the product of the Hessian of the
C objective function times an arbitrary vector will be computed. If
C the user has not been implemented the user-supplied evalhd
C subroutine to do this task then htvtype argument must be set to 1
C (ONE). In this case an internal subroutine that approximates this
C product by incremental quotients will be used. Note that, even in
C this case, evalhd subroutine must be present (with an empty body).
C This is the default option and the empty-body subroutine follows:
C
C subroutine evalhd(nind,ind,n,x,m,lambda,rho,d,hd,flag)
C
C SCALAR ARGUMENTS
C integer nind,n,m,flag
C
C ARRAY ARGUMENTS
C integer ind(nind)
C double precision d(n),hd(n),lambda(m),rho(m),x(n)
C
C flag = - 1
C
C end
C
C If, on the other hand, the user prefers to implement his/her own
C evalhd subroutine then htvtype argument must be set to 0 (ZERO).
C In this case, the product of the Hessian times vector d (input
C argument of evalhd subroutine) must be saved in vector hd (output
C argument of evalhd subroutine). The other arguments description as
C well as some hints on how to implement your own evalhd subroutine
C can be found in the GENCAN arguments description.
C When ALGENCAN uses GENCAN to solve the subproblems in the classical
C Augmented Lagrangian framework, ALGENCAN uses its own evalhd
C subroutine to overcome the lack of continuity of the second
C derivatives. So, when GENCAN is being used toghether with ALGENCAN,
C htvtype must be equal to 0 (ZERO). On the other hand, if GENCAN is
C being used stand-alone, just set htvtype equal to 1 (ONE) and add
C the empty-body subroutine described above.
htvtype = 1
C ARGUMENTS RELATED TO STOPPING CRITERIA
C Besides the stopping criterion related to the sup-norm of the
C continuous projected gradient, there is another stopping criterion
C related to its Euclidian norm. So, GENCAN stops the process if it
C finds a point at which the Euclidian norm of the continuous
C projected gradient is smaller than epsgpen.
epsgpen = 0.0d0
C For an explanation of maxitngp see above the explanation of tmax
C in ''DIMENSIONS FOR SOME WORKING SPACES''. Just note that the
C value of maxitngp must be less than or equal to tmax.
maxitngp = tmax
C maxitnfp means MAXimum of allowed number of iterations with No
C Progress in the objective functional value. ''Progress'' from one
C iteration to the next one refers to ( fnew - fprev ). Since the
C begining of the algorithm we save the ''best progress'' and
C consider that there was no progress in an iteration if the
C progress of this iterations was smaller than epsnfp times the best
C progress. Finally, the algorithm stops if there was no progress
C during maxitnfp consecutive iterations.
maxitnfp = maxit
epsnfp = 0.0d0
C There is a stopping criterion that stops the method if a point
C with a functional value smaller than fmin is found. The idea
C behind this stopping criterion is to stop the method if the
C objective function is not bounded from below.
fmin = 1.0d-05
C ARGUMENTS RELATED TO CONJUGATE GRADIENTS
C When computing the Truncated Newton direction by Conjugate
C Gradients there is something similar to a ''trust-region radius''.
C This trust radius is updated from iteration to iteration depending
C on the agreement of the objective function and its quadratic
C model. But an initial value for the trust radius is required. If
C the user has a good guess for this initial value then it should be
C passed to GENCAN using the delta0 arguments. On the other hand, if
C delta0 is set to -1, a default value depending on the norm of the
C current point will be used.
delta0 = - 1.0d0
delmin = 1.d-2
c delta0 = delmin
C The ''trust-region'' can be like a ball (using Euclidian norm) or
C like a box (using sup-norm). This choice can be made using trtype
C (TRust region TYPE) argument. trtype equal to 0 means Euclidian
C norm and trtype equal to 1 means sup-norm.
trtype = 1
C When the method is far from the solution, it may be not useful to
C do a very large effort in computing the Truncated Newton direction
C precisely. To avoid it, a fixed maximum number of iterations for
C Conjugate Gradients can be given to GENCAN. If the user would like
C to choose this maximum number of iterations for Conjugate
C Gradient then it should use the cgmaxit arguments. On the other
C hand he/she prefers to leave this task to GENCAN then he/she
C should set cgmaxit to -1.
cgmaxit = -1
C If the task of deciding the accuracy for computing the Truncated
C Newton direction is leaved to GENCAN then a default strategy based
C on increasing accuracies will be used. The proximity to the
C solution is estimated observing the norm of the projected gradient
C at the current point and locating it between that norm at the
C initial point and the expected value of that norm at the solution.
C Then the accuracy for the Truncated Newton direction of the
C current iteration will be computed taking a precision located in
C the same relative position with respect to two given values for
C the accuracies for the first and the last Truncated Newton
C direction calculations. These two accuracies (cgepsi and cgepsf,
C respectively) must be given by the user. Moreover, the expected
C value of the projected gradient norm at the solution (cggpnf) must
C also be given by the user who must indicate setting argument
C cgscre to 1 or 2 if that norm is the Euclidian or the sup-norm.
cggpnf = max( 1.0d-04, max( epsgpen, epsgpsn ) )
cgscre = 2
cgepsi = 1.0d-01
cgepsf = 1.0d-05
C The next two arguments are used for an alternative stopping
C criterion for Conjugate Gradients. Conjugate Gradients method is
C stopped if the quadratic model makes no progress during maxitnqmp
C (MAXimum of ITerations with No Quadratic Model Progress)
C consecutive iterations. In this context, ''no progress'' means
C that the progress is smaller than epsnqmp (EPSilon to measure the
C No Quadratic Model Progress) times the best progress obtained
C during the previous iterations.
epsnqmp = 1.0d-04
maxitnqmp = 5
C Depending on how much the objective function seems to be a
C quadratic, function, Conjugate Gradients may take different
C decision. So, if the objective function is a quadratic function or
C is very similar to a quadratic function then the nearlyq argument
C should be set to TRUE, else, it should be set to FALSE. However,
C the option with nearlyq equal TRUE never showed good results.
C Regarding this unexpected no good performance, rather recently it
C was found a bug that affected the behaviour of GENCAN just in this
C case (See the April 1st, 2003 modifications report at the end of
C this file). So, new experiments setting nearlyq equal TRUE should
C be made.
nearlyq = .false.
C FINALLY, CALL GENCAN
call gencan(n,x,l,u,m,lambda,rho,epsgpen,epsgpsn,maxitnfp,epsnfp,
+maxitngp,fmin,maxit,maxfc,delta0,cgmaxit,cgscre,cggpnf,cgepsi,
+cgepsf,epsnqmp,maxitnqmp,nearlyq,nint,next,mininterp,maxextrap,
+gtype,htvtype,trtype,iprint,ncomp,f,g,gpeucn2,gpsupn,iter,fcnt,
+gcnt,cgcnt,spgiter,spgfcnt,tniter,tnfcnt,tnstpcnt,tnintcnt,
+tnexgcnt,tnexbcnt,tnintfe,tnexgfe,tnexbfe,inform,wd(1),wd(n+1),
+wd(2*n+1),wi,lastgpns,wd(3*n+1),eta,delmin,lspgma,lspgmi,theta,
+gamma,beta,sigma1,sigma2,sterel,steabs,epsrel,epsabs,infrel,
+infabs)
end
C ******************************************************************
C ******************************************************************
C Last update of GENCAN or any of its dependencies:
C
C February 18th, 2005.
C
C See report of modifications at the end of this file.
subroutine gencan(n,x,l,u,m,lambda,rho,epsgpen,epsgpsn,maxitnfp,
+epsnfp,maxitngp,fmin,maxit,maxfc,udelta0,ucgmaxit,cgscre,cggpnf,
+cgepsi,cgepsf,epsnqmp,maxitnqmp,nearlyq,nint,next,mininterp,
+maxextrap,gtype,htvtype,trtype,iprint,ncomp,f,g,gpeucn2,gpsupn,
+iter,fcnt,gcnt,cgcnt,spgiter,spgfcnt,tniter,tnfcnt,tnstpcnt,
+tnintcnt,tnexgcnt,tnexbcnt,tnintfe,tnexgfe,tnexbfe,inform,s,y,d,
+ind,lastgpns,w,eta,delmin,lspgma,lspgmi,theta,gamma,beta,sigma1,
+sigma2,sterel,steabs,epsrel,epsabs,infrel,infabs)
implicit none
C SCALAR ARGUMENTS
logical nearlyq
integer cgcnt,cgscre,fcnt,gcnt,gtype,htvtype,inform,iprint,iter,m,
+ maxextrap,maxfc,maxit,maxitnfp,maxitngp,maxitnqmp,
+ mininterp,n,ncomp,spgfcnt,spgiter,tnexbcnt,tnexbfe,
+ tnexgcnt,tnexgfe,tnfcnt,tnintcnt,tnintfe,tniter,tnstpcnt,
+ trtype,ucgmaxit
double precision beta,cgepsf,cgepsi,cggpnf,delmin,epsabs,epsgpen,
+ epsgpsn,epsnfp,epsnqmp,epsrel,eta,f,fmin,gamma,gpeucn2,
+ gpsupn,infabs,infrel,lspgma,lspgmi,next,nint,sigma1,
+ sigma2,steabs,sterel,theta,udelta0
C ARRAY ARGUMENTS
integer ind(n)
double precision d(n),g(n),l(n),lambda(m),lastgpns(0:maxitngp-1),
+ rho(m),s(n),u(n),w(5*n),x(n),y(n)
C Solves the box-constrained minimization problem
C
C Minimize f(x)
C
C subject to
C
C l <= x <= u
C
C using a method described in
C
C E. G. Birgin and J. M. Martinez, ''Large-scale active-set box-
C constrained optimization method with spectral projected
C gradients'', Computational Optimization and Applications 23, pp.
C 101-125, 2002.
C
C Subroutine evalal must be supplied by the user to evaluate the
C objective function. The prototype of evalal subroutine must be
C
C subroutine evalal(n,x,m,lambda,rho,f,flag)
C
C C On Entry:
C C
C C n integer
C C number of variables
C C
C C x double precision x(n)
C C current point
C C
C C m integer
C C number of constraints (equalities plus inequalities)
C C
C C lambda double precision lambda(m)
C C current estimation of the Lagrange multipliers
C C
C C rho double precision rho(m)
C C penalty parameters
C C
C C NOTE: arguments m, lambda and rho are useful when GENCAN is
C C being used for solving the box-constrained subproblems of an
C C Augmented Lagrangian framework. When GENCAN is being used
C C stand-alone for solving a bound-constrained problem, these
C C arguments are dummy arguments and must be ignored.
C C
C C On Return
C C
C C f double precision
C C objective function value at x
C C
C C flag integer
C C 0 means ''no errors''
C C any other value means ''there was an error in the
C C objective function calculation''.
C C
C C SCALAR ARGUMENTS
C integer flag,m,n
C double precision f
C
C C ARRAY ARGUMENTS
C double precision lambda(m),rho(m),x(n)
C
C C ''Here it should be the body of evalal subroutine that saves
C C in f the objective function value at x. Moreover, it sets
C C flag equal to 0 if the calculation was successfully done and
C C sets flag equal to any other value different from 0 if the
C C objective function is not well defined at the current point
C C x.''
C
C end
C
C Subroutine evalnal to calculate the gradient of the objective
C function may be supplied by the user or not, depending on the
C value of gtype argument (gtype equal to 0 means that the evalnal
C subroutine will be supplied by the user and gtype equal to 1 means
C that an internal GENCAN subroutine will be used to estimate the
C gradient vector by central finite differences). In any case, a
C subroutine named evalnal with the following prototype must
C present.
C
C subroutine evalnal(n,x,m,lambda,rho,g,flag)
C
C C On Entry:
C
C C n integer
C C number of variables
C C
C C x double precision x(n)
C C current point
C C
C C m integer
C C number of constraints (equalities plus inequalities)
C C
C C lambda double precision lambda(m)
C C current estimation of the Lagrange multipliers
C C
C C rho double precision rho(m)
C C penalty parameters
C C
C C NOTE: arguments m, lambda and rho are useful when GENCAN is
C C being used for solving the box-constrained subproblems of an
C C Augmented Lagrangian framework. When GENCAN is being used
C C stand-alone for solving a bound-constrained problem, these
C C arguments are dummy arguments and must be ignored.
C C
C C On Return
C C
C C g double precision g(n)
C C gradient of the objective function at x
C C
C C flag integer
C C 0 means ''no errors'',
C C any other value means ''there was an error in the
C C gradient calculation''.
C C
C C SCALAR ARGUMENTS
C integer flag,m,n
C
C C ARRAY ARGUMENTS
C double precision g(n),lambda(m),rho(m),x(n)
C
C C ''Here it should be the body of evalnal subroutine that
C C saves in g the gradient vector of the objective function at
C C x. Moreover, it sets flag equal to 0 if the calculation was
C C successfully done and sets flag equal to any other value
C C different from 0 if the gradient vector is not well defined
C C at the current point x. If GENCAN gtype argument was setted
C C to 1, i.e., the finite difference approximation provided by
C C GENCAN will be used, then this subroutine must even be
C C present for compilation purpose but it will never be
C C called.''
C
C end
C
C Subroutine evalhd to calculate of the Hessian of the objective
C function times a given vector may be supplied by the user or not,
C depending on the value of htvtype argument (htvtype equal to 0
C means that the evalhd subroutine will be supplied by the user and
C htvtype equal to 1 means tha an internal GENCAN subroutine will be
C used to estimate the product by incremental quotients). In any
C case, a subroutine named evalhd with the following prototype must
C present.
C
C subroutine evalhd(nind,ind,n,x,m,lambda,rho,d,hd,flag)
C
C C On Entry:
C C
C C nind integer
C C number of component of the Hessian-vector product that
C C must be computed
C C
C C ind integer ind(nind)
C C the component that must be computed are ind(1)-th ...
C C ind(nind)-th
C C
C C n integer
C C number of variables
C C
C C x double precision x(n)
C C current point
C C
C C m integer
C C number of constraints (equalities plus inequalities)
C C
C C lambda double precision lambda(m)
C C current estimation of the Lagrange multipliers
C C
C C rho double precision rho(m)
C C penalty parameters
C C
C C NOTE: arguments m, lambda and rho are useful when GENCAN is
C C being used for solving the box-constrained subproblems of an
C C Augmented Lagrangian framework. When GENCAN is being used