- Lecturer: Prof. Stefania Petra
- Exercises: Stefania Petra, Matthias Zisler
- No in-person lecture.
- Short videos that explain each subtopic from a top-down viewpoint.
- Detailed lecture notes that you read on your own.
- Exercise sheets you work on your own. Solutions will be discussed in Zoom.
- Language: English
- SWS: 4
- ECTS: 6 + 2
- Lecture Id: MM35, Spezialisierungsmodul Numerik und Optimierung
- Supplementary Practical: For participating in the optional Programming Project in the semester break you get two extra credits.
- Prior Knowledge: Required: Lineare Algebra and Analysis
The lecture gives an introduction into the field of convex optimization and details the most important numerical methods for the solution of convex optimization problems.
- Preliminaries: Convex sets, convex functions, convex optimization problems (LPs, QPs, SOCPs, SDPs)
- Theory: Separation theorems, duality, subdifferential calculus, existence and optimality
- Algorithms: Gradient-based methods for smooth optimization, proximal-point and splitting methods
- Applications: Convex models in mathematical imaging
- week 2, Examples of Convex Sets: Hyperplanes, Linear Subspaces, Affine and Convex Hulls, Simplices will be presented offline on Wednesday 11.11 Slides Video
- R.T. Rockafellar, R.J.-B. Wets, Variational Analysis, Springer, 2004
- R. Rockafellar. Convex Analysis. Princeton Univ. Press, 1970
- A. Auslender, M. Teboulle, Asymptotic Cones and Functions in Optimization and Variational Inequalities, Springer, 2003
- S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004
- A. Ben-Tal, A. Nemirovski, Lectures on Modern Convex Optimization, SIAM, 2001
- Y. Nesterov. Introductory Lectures on Convex Optimization. Kluwer Acad. Publ., 2004
- H. H. Bauschke and P. L. Combettes. Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, 2nd edition, 2017
Link for Tutorial
Meeting ID: 870 1356 7712 Passcode: 488223
You are supposed to solve at least 50% of the numerical exercises (Matlab, Pyhton) in order to participate in the exam. There will be no points, only “OK”, “Not OK” or “ ” if nothing was handed in
- week 5, Sheet 4 will be discussed on Thur. 03.12, 14:15-15:45, via Zoom