Convex Optimization

  • Exercises: Stefania Petra, Matthias Zisler
  • Format:
    • 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.
  • Registration: Please register in Müsli and Moodle.
  • Prior Knowledge: Required: Lineare Algebra and Analysis

Content

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

Lecture Notes

Literature

  • 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

Exercises

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

Introduction to Matlab and CVX

CVX and Python

Solutions to Practical Exercises