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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] |
| (plan) 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] |
Homeworks: PDF
Literature:
