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Convex Optimization
Last Updated: 2026-02-05 14:57:24
Abstract
Convex optimization encompasses in a balanced manner theory (convex analysis, optimality conditions, duality theory) and algorithms for convex optimization. In particular the recent theory of semidefinite programming is discussed.
Content
Convexity plays a central role in the design and analysis of modern and highly successful algorithms for solving real-world optimization problems. The lecture (in English) on convex optimization will treat in a balanced manner theory (convex analysis, optimality conditions) and algorithms for convex optimization. Beginning with basic concepts and results about the structure of convex sets, continuity and differentiability of convex functions (including conjugate functions), the lecture will cover systems of inequalities, the minimum (or maximum) of a convex function over a convex set, Lagrange multipliers, duality theory and mini-max theorems. On the algorithmic part, we will cover efficient algorithms based on interior-point methods in the framework of self-concordant functions. In this way, we will obtain a simple algorithm for semi-definite optimization. Thus we will be discussing one of the most challenging research areas of nonlinear optimization for which there are many interesting open questions both in theory and practice. The lecture will follow the (unpublished) textbook by S. Boyd, Convex Optimization, made available on the net.
General Information
- Language
- English
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Convex Optimization |
|
2 h weekly |
| exercise |
Convex Optimization
im Wechsel mit 401-3902-00 U Diskrete Optimierung
|
|
1 h weekly |