On various notions of regularity of sets in nonsmooth analysis
Nonlinear Analysis: Theory, Methods & Applications
Variational pairs and applications to stability in nonsmooth analysis
Nonlinear Analysis: Theory, Methods & Applications
Coderivative Analysis of Variational Systems
Journal of Global Optimization
SIAM Journal on Optimization
Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces
SIAM Journal on Optimization
Lipschitz behavior of solutions to nonconvex semi-infinite vector optimization problems
Journal of Global Optimization
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This paper deals 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.