## Convex Optimization

Module Number: EI7435

Duration: 1 Semester

Occurence: Winter Semester

Language: English

Number of ECTS: 6

## Staff

Professor in charge: Wolfgang Utschick

## Amount of work

Contact hours:60

Self-study hours: 120

Total: 180

## Description of achievement and assessment process

Written examination (evaluation of basic theoretical concepts presented in the lecture and tutorials). Up to 20% of the examination can be conducted in the form of multiple choice questions.

**Exam type: **written

**Exam duration (min.): **90

**Possibility of retaking:** In the next semester: Yes. At the end of the semester: No

**Homework:** No

**Lecture**: No

**Conversation:** No

**Written paper:** No

## Recommended requirements

Basic Classes in Linear Algebra and Calculus.

## Contents

Introduction: - basic definitions and fundamentals- problem statement Convex analysis: - convex sets - convex functionsLinear programming: - extremal points and directions - simplex algorithm Optimality conditions: - Fritz John conditions - Karush-Kuhn-Tucker conditions - constraint qualifications Lagrangian duality: - duality theorems Algorithms:- general concept - unconstrained optimization- constrained optimization Solutions for the dual problem: - subgradient method- cutting plane algorithm Interior-point method: - barrier functions - IP algorithmApplications: - problems from multiuser information theory - resource allocation - parameter optimization in layered and distributed communication systems

## Study goals

At the end of the module, students are able to remember, understand and apply the theory, the basic methodologies and algorithms of convex optimization theory, and students are able to analyse and evaluate technical systems from the perspective of optimization theory and are able to create mathematical concepts and numerical algorithms for the optimal design and operation of information and communications systems.

## Teaching and learning methods

- Learning method: In addition to the individual methods of the students, consolidated knowledge is aspired by repeated lessons in exercises and tutorials.
- Teaching method: During the lectures, the students are instructed in a teacher-centered style. The exercises are held in a student-centered way.

## Media formats

The following kinds of media are used:

- Presentations
- Lecture notes
- Exercises with solutions as download

## Literature

The following literature is recommended:

- M. S. Bazaara, H. D. Sherali and C. M. Shetty. Nonlinear Programming: Theory and Algorithms. Wiley, 2006
- D. Bertsekas and A. Nedic. Convex Analysis and Optimization. Athena Scientific, 2003
- S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge, 2004