Convex Optimization

Summer Semester 2019

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 funtions
• Constrained miminimzation 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.
• Actual exercise sheet: –

Final exam: 24 July 2019, 10 am in H1

Literature:

• V. Barbu and Th. Precupanu, Convexity and Optimization in Banach Spaces
• I. Ekeland and R. Teman, Convex Analysis and Variational Problems
• H. Bauschke and 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