Generalized Differential Calculus for Nonsmooth and Set-Valued Mappings

We study some generalized differentiability concepts for multifunctions and non-smooth mappings in finite dimensions. The most attention is paid to the so-called coderivative of multifunctions introduced earlier by the author. This coderivative has many useful applications to optimization and control problems, to sensitivity analysis for generalized equations and variational inequalities, etc. In this paper we develop a rich calculus for the coderivative and related subdifferential constructions using an extremal (variational) approach.