This monograph presents the most important results of a new branch of functional analysis: subdifferential calculus and its applications. New tools and techniques of convex and nonsmooth analysis are presented, such as Kantorovich spaces, vector duality, Boolean-valued and infinitesimal versions of nonstandard analysis, etc., covering a wide range of topics.
This volume fills the gap between the theoretical core of modern functional analysis and its applicable sections, such as optimization, optimal control, mathematical programming, economics and related subjects.
The material in this book will be of interest to theoretical mathematicians looking for possible new applications and applied mathematicians seeking powerful contemporary theoretical methods.

Preface. 1. Convex Correspondences and Operators. 2. Geometry and Subdifferentials. 3. Convexity and Openness. 4. The Apparatus of Subdifferential Calculus. 5. Convex Extremal Problems. 6. Local Convex Approximations. References. Author Index. Subject Index. Symbol Index.