Nonconvex differential calculus for infinite dimensional multifunctions

Abstract

The paper is concerned with generalized differentiation of set-valued mappings between Banach spaces. Our basic object is the so-called coderivative of multifunctions that was introduced earlier by the first author and has had a number of useful applications to nonlinear analysis, optimization, and control. This coderivative is a nonconvex-valued mapping which is related to sequential limits of Fréchet-like graphical normals but is not dual to any tangentially generated derivative of multifunctions. Using a variational approach, we develop a full calculus for the coderivative in the framework of Asplund spaces. The latter class is sufficiently broad and convenient for many important applications. Some useful calculus results are also obtained in general Banach spaces