## Convez Optimization Laboratory

Module Number: EI7256

Duration: 1 Semester

Occurence: Summer semester

Language: English

Number of ECTS: 6

## Staff

Professor in charge: Wolfang Utschick

## Amount of work

Contact hours: 150

Self-studying hours: 30

Total: 180

## Description of achievement and assessment methods

- final examination (evaluation of basic theoreticl concepts behind the individual projects and implementation-related issues)
- pass/fail credit requirement: 6 programming projects (in-depth understanding by programming related algorithms and evaluating practical scenarios)

**Exam type**: oral

**Exam duration**: 30 min.

**Possibility of re-taking:** in the next semester: Yes; at the end of the semester: No

**Homework**: No

**Lecture**: No

**Conversation:** No

**Written paper:** Yes

## Recommended requirements

Working knowledge about convex optimization theory and algorithms as presented in the Optimization in Communications Engineering course. Working knowledge in fundamentals of communications engineering and signal processing. Working knowledge in the programming language MATLAB.

## Contents

This laboratory provides insights and practical instructions for designing algorithms in the field of communications engineering and signal processing based on mathematical optimization theory by a series of successive teaching and hands-on units. Each unit includes the understanding and analysis of a typical problem of the addressed application scenarios, its mathematical modeling and the design and implementation of an adequate solution. Designed algorithms from a previous unit of the laboratory are supposed to be reused.

The addressed topics will cover

- CVX
- disciplined convex problems rules
- gradient methods
- linear programming
- interior-point method
- Lagrangian dualty
- dual decpomostion method
- subgradient method
- cutting-plane methods
- conic optimization
- SDTP3
- Sedumi
- non-convex optimization

## Study goals

At the end of the module students are able to understand and analyse typical optimization problems in the field of communications engineering and signal processing by means of mathematical modeling from a mathematical optimization perspective and to apply, analyse, evaluate and create algorithms for the numerical solution of these optimization problems. The students are further able to apply state-of-the-art general purpose solvers for convex optimization problems.

## Teaching and learning methods

Provided with written instructions for each laboratory unit the students work out a thome a solution for the given problem, consisting of a mathematical model, a solution concept and the conception and implementation of the algorithm. Teaming up is supported. After the presentation and discussion of the outcomes the next unit starts. In the final unit of the laboratory the students deal with a more complex problem of the introduced application scenarios.

## Media formats

Presentations and laboratory instructions

## Literature

The following references are recommended:

- W. Utschick and L. Gerdes: Optimization in Communciations Engineering, Lecture Notes, 2012
- 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