Generalized differentiation of parameter-dependent sets and mappings.

This article concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings and nonsmooth functions), which naturally appear, e.g. in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this article. [ABSTRACT FROM AUTHOR]