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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

Convex analysis Script of Prof. G. Wanka

Convex optimization Script of Prof. J. Peypouquet