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I teach the lecture together with M. Loebl.
The lecture is scheduled on Monday at 14:00 in S7.
The tutorial is done by means of homeworks and consultations, so ignore the official schedule.
Done:
| 3.10. | Reminder of convexity: convex sets, convex functions and convex optimization. Quasiconvex functions: definition, examples, sublevel set and first order characterizations. Chain rules for quasiconvexity: maximum, composition. |
| 10.10. | Chain rules for quasiconvexity: product, division. Quasiconvex optimization: local and global solutions, convexity of the optimal solution set, optimality condition. Generalized linear fractional programming and application in von Neumann economic growth model. Pseudoconvexity: relation to convexity and quasiconvexity, pseudoconvex optimization: optimality conditions. |
| 17.10. | Reminder of Farkas lemma. Gordan theorem. Necessary optimality conditions: Conditions of Fritz John, Karush-Kuhn-Tucker (KKT) conditions. Constraint qualifications for KKT: linear independence, Slater condition and Abadie condition. |
| 24.10. |
KKT and linear approximation, KKT for linear and quadratic programming, Sufficient KKT conditions. Lagrange duality: dual function and dual problem, weak duality theorem, geometric interpretation, bounds for the optimal value. |
| 31.10. | Lagrange duality: strong duality under the Slater condition, examples of (non-)strong duality, duality for linear programming, sensitivity analysis and shadow prices, saddle point interpretation. |
| 7.11. | Lagrange duality for convex quadratic programming and semidefinite programming. Application: Support vector machines. |
| 14.11. | Cardinality problems and L1-norm approximation: examples, interpretation of the approximation, simple methods, rank minimization. |
Homeworks: PDF
Literature:
