The paper 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 paper.
Number in Series
Applied Mathematics | Mathematics
AMS Subject Classification
Primary: 49J52, 49J53; Secondary: 90C29
Mordukhovich, Boris S. and Wang, Bingwu, "Generalized Differentiation of Parameter-Dependent Sets and Mappings" (2006). Mathematics Research Reports. 43.