Syllabus
Nonconvex nonsmooth analysis
1) Variational geometry nonconvex sets. (Several types of normal cones and their relations).
2) Subdiferentials and coderivatives (Fréchet, proximal, Clarke, Mordukhovich).
3) First order calculus with relaxed constraint qualification based on chain rules.
4) Second order calculus (derivatives of compositions for polyhedral and conic constraint systems).
5) Applications: Optimality conditions, stability analysis of multifunction, error bound property, nonsmooth numerical methods.
Annotation
The lecture builds up base of modern optimization and equilibria theory.