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I teach the lecture jointly with Martin Loebl.
The lecture is scheduled on Thursdays at 15:40 in S221 (2nd-floor corridor).
The tutorials will be conducted via homework and consultations, so you can ignore the official schedule.
Schedule of lectures:
| 1.10. |
Convexity review: convex sets, convex functions, convex optimization. Quasiconvex and explicitly quasiconvex functions: definitions, examples, characterization using sublevel sets and first derivatives. Chain rules for quasiconvexity: maximum and division. [textbook: chapter 1 and sections 3.1-3.2] |
| 8.10. |
Chain rules for quasiconvexity: product and composition. Quasiconvex functions in optimization: a strict local minimum is global, the set of optimal solutions is convex, optimality condition. Generalized linear fractional programming and the von Neumann growth model. Pseudoconvex functions: relationship to convex and quasiconvex functions, optimality conditions in pseudoconvex optimization. [textbook: sections 3.2-3.5] |
| 15.10. |
Recap of Farkas' Lemma, Gordan's Theorem. Necessary optimality conditions: Fritz John conditions, Karush–Kuhn–Tucker (KKT) conditions. Constraint qualifications for KKT: linear independence, Slater's condition, and Abadie's condition.
[textbook: sections 4.1-4.2] |
| 22.10. |
KKT conditions and linearization, sufficient KKT conditions for optimality, the form of the KKT conditions for linear and quadratic programming. An application for sparsemax activation function in neural networks. Lagrangian duality: the dual function and the dual problem, weak duality, geometric interpretation, bounds on the optimal value. [textbook: sections 4.2-4.3, 5.1] |
| (plan) 29.10. |
Lagrange Duality: Strong duality, examples, and sensitivity analysis.
[textbook: sections 5.2-5.3] |
Homeworks: PDF
Literature:
