Fachbereich Mathematik 
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Optimization (Summer term 2022)

We will give with this lecture an introduction to basics of convex optimization theory in infinite dimensional spaces. In particular, the following properties are covered

  • Convex functions
  • Constrained minimization problems
  • Convex conjugates
  • Proximal maps
  • Primal and dual problem formulation
  • Minimization schemes, in particular splitting approaches

Exercises:

  • One exercises sheet per week;
  • Minimum 60 % of the exercises required for participating at the final exam.

Final exam:


Literature:

    V. Barbu & Th. Precupanu, Convexity and optimization in Banach spaces
    I. Ekeland & R. Teman, Convex analysis and variational problems
    H. Bauschke & P. Combettes, Convex analysis and monotone operator theory in Hilbert spaces
    J. Peypouquet, Convex optimization in normed spaces: theory, methods and examples
    M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich, Optimization with PDE Constraints (only used for Descent methods)

Other useful material


 
  Seitenanfang  Impress 2022-02-21, Christina Brandt