Stability of set-valued mappings in infinite dimensions: Point criteria and applications

This paper dears with effective characterizations of stability and regularity properties of set-valued mappings in infinite dimensions, which are of great importance for applications to many aspects in optimization and control. The main purpose is to obtain verifiable necessary and sufficient conditions for these properties that are expressed in terms of constructive generalized differential structures at reference points and are convenient for applications. Based on advanced techniques in nonsmooth analysis, new dual criteria are proven in this direction under minimal assumptions. Applications of such point conditions are given to sensitivity analysis for parametric constraint and variational systems which describe sets of feasible and optimal solutions to various optimization and related problems.