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In recent years Convex Analysis has become an important tool in image and data processing. This lecture introduces Convex Analysis and in particular optimization algorithms for solving convex variational problems.

The lecture will cover the following topics:

1. Convex sets
2. Convex functions and proximal mappings
3. Subdifferentials
4. Proximal algorithms
5. Monotone set-valued mappings
6. Conjugate functions
7. Duality theory
8. Primal-dual algorithms