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Fall 2016-2019

The main topics here are convex sets, convex functions, KKT optimality conditions and duality. The presentations are made in classical manner and give basic facts on the topics.

  1. Introduction (ru, en).

  2. Convex sets (ru, en)

  3. Projection onto set, separation, support hyperplane (ru, en)

  4. Conjugate sets. Farkas' lemma (ru, en)

  5. Introduction to matrix calculus (ru, en)

  6. Convex functions (ru, en)

  7. Subdifferential (ru, en)

  8. Feasible direction cone, tangent cone, sharp extremum (ru, en)

  9. Conjugate functions (ru, en) + smoothing demo Open In Colab

  10. Optimality conditions (ru, en)

  11. Introduction to duality theory (ru, en)