Convex Optimization
Summer Semester 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 funtions
- Constrained miminimzation problems
- Convex conjugates
- Proximal maps
- Primal and dual problem formulation
- Minimization schemes, in particular splitting approaches
In the first 7 weeks, the course will be given together with the course "Convex Optimization & Applications". You thus need to decide for one of the two course options!
There is only one common Moodle course named "Convex optimization & applications" for both courses. Please register to this course in Moodle (password provided in Stine).
Exercises:
- One exercises sheet per week
- Minimum 60 % of the exercises required for participating at the final exam.
Final exam for the "Optimization course" ( the first part of the lecture): 30.5. 2022 and 25.7. 2022
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