Convex Optimization
Summer Semester 2023
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
The course is also part of the course "Variational methods for inverse problems", i.e. students registered for that course will attend also the lectures on convex optimization. You thus need to decide for one of the two course options!
There is only one common Moodle course named "Convex optimization & Inverse problems" for both courses. Please register to this course in Moodle (different passwords for each course are 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": 17.7.23 H2 (first round), 10.8.23 H2 (second round)
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