Written exam (in case of a small number of participants: oral tests)

Convex optimization problems arise quite naturally in many application areas like signal processing, machine learning, image processing, communication and networks and finance etc. The course will give an introduction into convex analysis, the theory of convex optimization such as duality theory, algorithms for solving convex optimization problems such as interior point methods but also the basic methods in general nonlinear unconstrained minimization, and recent first-order methods in non-smooth convex optimization. We will also cover related non-convex problems such as d.c. (difference of convex) programming, biconvex optimization problems and hard combinatorial problems and their relaxations into convex problems. While the emphasis is given on mathematical and algorithmic foundations, several example applications together with their modeling as optimization problems will be discussed. The course requires a good background in linear algebra and multivariate calculus, but no prior knowledge in optimization is required.

Students learn the foundations of convex analysis and how to formulate and transform optimization problems. After the lecture they know a variety of methods for solving convex and non-convex optimization problems and have guidelines which method to choose for which problem.

The lecture does not follow a specific book. The literature for this lecture will be provided at the beginning of the semester.