Variational analysis of extended generalized equations via coderivative calculus in Asplund spaces

Abstract

This paper is devoted to the development of variational analysis and generalized differentiation in the framework of Asplund spaces. We mainly concern the study of a special class of set-valued mapping given in the form S ( x ) = { y ∈ Y | 0 ∈ F ( x , y ) + Q ( x , y ) } , x ∈ X , where both F and Q are set-valued mappings between Asplund spaces. Models of this type are associated with solutions maps to the so-called (extended) generalized equations and play a significant role in many aspects of variational analysis and its applications to optimization, stability, control theory, etc. In this paper we conduct a local variational analysis of such extended solution maps S and their remarkable specifications based on dual-space generalized differential constructions of the coderivative type. The major part of our analysis revolves around coderivative calculus largely developed and implemented in this paper and then applied to establishing verifiable conditions for robust Lipschitzian stability of extended generalized equations and related objects.