Convex Optimization

Lecturer: Wolfgang Utschick with Benedikt Böck

Target Audience: Master EI and MSCE

Language: English

Next Exam: tbd (no responsibility is taken for the correctness of this information)

Additional Information: TUMonline and Moodle

Lectures/Tutorials in Winter Semester 2024/25

Content

Introduction: Problem Statement of Optimization, Basic Definitions, Categorization.

Convex Analysis: Convex Sets and Functions.

Linear Programming: Extremal points, Extremal directions.

Optimality Conditions: Karush-Kuhn-Tucker Conditions, Constraint Qualifications.

Lagrangian Duality: Duality Theorems, Solutions for the Primal and Dual Problem.

Algorithms: Subgradient Methods, Cutting Plane Algorithms, Projection Methods, Fixpoint Algorithms.

Applications: Network Optimization, Problems from Multiuser Information Theory, Resource Allocation, Parameter Optimization in Layered/Distributed Communication Systems.