Convex Optimization

  • Exercises: Stefania Petra, Matthias Zisler
  • Lecture room: 2.103 (Mathematikon)
  • Times: Wed 11.15-12.45 (lecture), Thu 14.15-15.45 (tutorial)
  • Format:
    • In-person lecture were we also 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 person.
    • We will use Microsoft Teams for communication and distributing lecture content.
  • 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 Teams.
  • Prior Knowledge: Required: Lineare Algebra and Analysis


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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 for non-smooth optimization
  • Applications: Convex models in mathematical imaging and data science


  • 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


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

Software Practical: Convex Optimization

The software practical is suited for students attending the lecture on Convex Optimization that additionally wish to apply the algorithms and concepts to concrete examples in order to get a deeper understanding.

Registration: in the lecture, or mail to Stefania Petra.