The course will be devoted to local and infinitesimal analysis of non-differentiable functions and mappings and set-valued mappings in (mainly) Banach spaces.
I plan to touch (if time permits) upon the following topics:
1) Slopes and subdifferentials
2) Tangents and normals. Fans and prederivatives
3) Subdifferential calculus
4) Integration of subdifferentials
5) Mean-value theorems
6) Openness, regularity and stability of set-valued mappings
7) Compactness and Fredholm-type properties
8) Applications to optimization