On variational analysis in infinite dimensions1
Boris S. Mordukhovich · 2022
Variational analysis has been recognized as an active area in mathematics that, on one hand, studies constrained optimization and related problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems which may not be of a variational nature. Nonsmooth functions, sets with nonsmooth boundaries, and set-valued mappings appear naturally and frequently in the framework of variational analysis and require the development of appropriate tools of generalized differentiation. This chapter concerns some aspects of variational analysis in infinite dimensional spaces. It presents recent results on basic principles in variational analysis, on generalized differentiation of nonsmooth and set-valued mappings, and on dual differential characterizations of Lipschitzian stability.