Convex Optimization & applications (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
Part 1
- Convex functions
- Constrained minimization problems
- Convex conjugates
- Proximal maps
- Primal and dual problem formulation
- Minimization schemes, in particular splitting approaches
Part 2
- 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!
Exercises:
- One exercises sheet per week;
- Minimum 60 % of the exercises required for participating at the final exam.
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