Analysis and applications of nonconvex subdifferential in infinite dimensions
Boris S. Mordukhovich, Yabin Shao · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1994
We study a class of nonconvex subdifferentials and related infinite dimensional constructions which have various applications to problems in optimization, sensitivity, and control. Despite the nonconvexity of their values, these constructions enjoy useful calculus properties in rather general infinite dimensional settings. The main tool to develop such a nonconvex calculus is an extremal principle which is related to necessary optimality conditions in nonsmooth optimization and can be viewed as a nonconvex analogue of the classical separation theorem. We provide applications of the calculus results obtained to characterizations of openness, metric regularity, and Lipschitzian properties of set-valued mappings important in nonsmooth optimization, sensitivity analysis, and related topics.