TEACHING

GENERAL INFORMATION

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. If time allows I will also cover d.c. (difference of convex) programming and convex problems as relaxations of hard combinatorial problems. While the emphasis is given on mathematical and algorithmic foundations, several example applications will be discussed.

The course requires a good background in linear algebra and calculus, but no prior knowledge in optimization is required. The course will follow in the first part mainly the book of Boyd and Vandenberge on "Convex Optimization" and can be seen as complementary to the core lecture "Optimization" which will also takes place during the summer semester.

Students who intend to do their master thesis in machine learning are encouraged to take this course.

Type: Advanced course (Vertiefungsvorlesung), 6 credit points

LECTURE MATERIAL

The course follows in the first part the book of Boyd and Vandenberghe.

The practical exercises will be in Matlab and will make use of CVX.

SLIDES AND EXCERCISES

LITERATURE AND OTHER RESOURCES

• The lecture will be based on the following book:
  S. Boyd and L. Vandenberghe: Convex Optimization, Cambridge University Press, (2004).
  The book is freely available
• Complementary book: D. P. Bertsekas: Nonlinear Programming, Athena Scientific, (1999).
• Other resources:
  • Matlab is available on cip[101-114] and cip[220-238].studcs.uni-sb.de, gpool[01-27].studcs.uni-sb.de
    The path is /usr/local/matlab/bin.
    For the sun workstations you have to select in the menu Applications/studcsApplications/Matlab
    Access from outside should be possible via ssh: ssh -X username@computername.studcs.uni-sb.de
  • Matlab tutorial by David F. Griffiths