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".

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

Conventional lectures on the blackboard supported by electronic media. The theory part closely follows the text book.

The lecture is held each Wednesday at 1:00pm in Sem. 389 (CG0118).

First class: March 1, 2023 at 1pm

oral exam

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

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

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