Syllabus
Nonsmooth convex analysis in finite dimension
1) Summary on convex sets and functions; Lipschitz continuity of functions; semicontinuity of functions
2) Modern version of convex separation theorems; extremal systems of sets
3) Geometry of convex sets: convex tangent and normal cones; convex calculus; basic properties of multifunctions
4) Convex subdifferential; calculus; support functions
5) Duality; Fenchel conjugates
6) Convex nonsmooth optimization problems: applications and source problems; existence of a solution; optimality conditions and constraint qualification (Slater CQ, LICQ, MFCQ, calmness CQ, Abadie CQ, Guignard CQ); duality in convex programming, selected subgradient methods
7) Nash games (NEP) and equilibria: applications and source problems; existence of a solution
Annotation
The lecture builds up base of modern optimization and equilibria theory.