STABILITY OF SET-VALUED MAPPINGS IN INFINITE DIMENSIONS - POINT CRITERIA AND APPLICATIONS

This paper dears with effective characterizations of stability and reg ularity properties of set-valued mappings in infinite dimensions, whic h are of great importance for applications to many aspects in optimiza tion and control. The main purpose is to obtain verifiable necessary a nd sufficient conditions for these properties that are expressed in te rms of constructive generalized differential structures at reference p oints and are convenient for applications. Based on advanced technique s in nonsmooth analysis, new dual criteria are proven in this directio n under minimal assumptions. Applications of such point conditions are given to sensitivity analysis for parametric constraint and variation al systems which describe sets of feasible and optimal solutions to va rious optimization and related problems.