• to acquire a familiarity with the basic convex theory
• to develop the skill of recognizing, formulating, and solving convex optimization problems
• to become able to read and understand recent research paper in signal processing, communications and information theory, which rely on the theory of convex optimization

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. 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 and communications

Time: Wednesday, 13:00-14:30 (starting March 1, 2017)

Place: SEM 389 (CG0118), Gußhausstraße 25/389

S. Boyd and L. Vandenberge, "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.