# 389.122 Convex Optimization for Signal Processing and Communications This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});});

2020S, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture

## Learning outcomes

After successful completion of the course, students are able to recognise and formulate convex optimisation programs for applications of signal processing, machine learnung, and communications, and to solve them. They are able to formulate the corresponding dual problem and the Karush-Kuhn-Tucker conditions. They are able to solve simple convex optimization programs numerically with the modelling language "cvx".

## Subject of course

Motivation

Convex optimization theory deals with how to optimally and efficiently solve a class of optimization problems. Although the theory of convex optimization theory dates back to the early twentieth century, it has found a rapidly increasing number of applications in the engineering sciences during the 1990s. This is largely due to the development of efficient algorithms for the solution of large classes of convex optimization problems but also due to an increased awareness of the theory. Today, many of the papers published in the signal processing and communications literature apply tools from convex optimization in solving and analyzing the relevant problems. The theory of convex optimisation is one of the mathematical foundations for machine learning. Thus, an understanding of convex optimization is necessary to understand the recent literature in either field. The theory part of the course will follow the book "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe. Applications and example will be taken directly from the recent literature on signal processing and communications.

Course topics

• the mathematical theory of convex functions and sets
• the concept of duality and generalized inequalities
• classical types of optimization problems
• algorithms for solving convex optimization problems
• applications in signal processing, machine learning, and communications

## Teaching methods

lectures in form of slide sets, following the text book.

## Mode of examination

Oral

All lectures are held on Wednesday 1pm via GoToMeeting:

https://global.gotomeeting.com/join/376353269

Recordings of the lectures are available on the following TUpeerTube channel:

https://tube1.it.tuwien.ac.at/video-channels/cvx/videos

All other materials (slides, notes, etc.) are provided on TISS

## Course dates

DayTimeDateLocationDescription
Wed12:30 - 14:3004.03.2020 - 11.03.2020Sem 389 Convex Optimization
Convex Optimization for Signal Processing and Communications - Single appointments
DayDateTimeLocationDescription
Wed04.03.202012:30 - 14:30Sem 389 Convex Optimization
Wed11.03.202012:30 - 14:30Sem 389 Convex Optimization

oral exam

## Course registration

Begin End Deregistration end
05.03.2020 00:00 04.07.2020 00:00

## Literature

Stephen Boyd and Lieven Vandenberghe, "Convex Optimization," Cambridge Univ. Press, 2004 (ISBN 0521833787).

Online available as pdf at http://www.stanford.edu/~boyd/cvxbook/

## Previous knowledge

The students are required to have a working knowledge of linear algebra and basic calculus. No previous knowledge of convex optimization is required.

English