Convex Optimization & Applications
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
- Algorithms based on forward backward splitting
- Algorithms based on primal dual splitting
- Semi-smooth Newton methods
- Application to variational regularization in imaging
- Outlook to non-convex optimization
In the first 7 weeks, the course will be given together with the course "Optimization" (part 1). 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).
- One exercises sheet per week
- Minimum 60 % of the exercises required for participating at the final exam.
Final exam : 25 July 2022, 2nd round in September
Exam for the "Optimization course" ( the first part of the lecture): 30.5. 2022 and 25.7. 2022
- 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