Convex and Set-Valued Analysis: Selected Topics

This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions, and properties of convex cones in infinite-dimensional spaces are discussed. The second part covers set-valued analysis, describes the properties of the Hausdorff metric and set-valued maps.