Convex Analysis and Nonsmooth Optimization
Convexity is an important property in Optimization. For instance, local and global optimal solutions coincide for a convex optimization problem. Many special classes of convex optimization problems can be solved approximately in polynomial time.
In this course we provide a systematic study of convex sets and convex functions. Convex optimization problems are investigated, in particular, an abstract duality theory is developed. We do not assume any kind differentiabilty and deal with subgradients, a generalization of derivatives.