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Optimization Techniques
Last Updated: 2026-02-05 14:59:53
Abstract
Mathematical discussion on diverse optimization techniques
Objective
Introduction to advanced topics in optimization theory and algorithms.
Content
1.Linear Optimization: Optimality and duality in linear programming, Pivot algorithms (the criss-cross method, the simplex method) and finiteness proofs, Farkas‘ Lemma and the linear feasibility problem, Sensitivity analysis, Geometry of convex polyhedra and pivot operations. 2.Combinatorial Optimization: Basic concepts of complexity theory (notions of P, NP and NP-complete), Optimization problems in graphs and networks, Integer programming formulations, Polynomial algorithms, Integrality of polyhedra, the Branch-and-Bound algorithm. Approximation algorithms, Column generation in Integer Programming. 3.Nonlinear Optimization: Basic concepts and algorithms for unconstrained optimization (descent methods, conjugate gradient and (Quasi-) Newton- method) with convergence analysis for the convex case. First and second order optimality condition for constrained optimization: Lagrange and Kuhn-Tucker theory. Complexity analysis of convex quadratic optimization using Interior Point Methods. Introduction to Semidefinite Programming.
General Information
- Language
- English
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Optimization Techniques |
|
2 h weekly |
| exercise | Optimization Techniques |
|
1 h weekly |