# Lipschitzian Stability of Parametric Constraint Systems in Infinite Dimensions

## Abstract

This paper mainly concerns applications of the generalized differentiation theory in variational analysis to robust Lipschitzian stability for various classes of parametric constraint systems in infinite dimensions including problems of nonlinear and nondifferentiable programming, implicit multifunctions, etc. The basic tools of our analysis involve coderivatives of set-valued mappings and associated limiting subgradients and normals for nonsmooth functions and sets. Using these tools, we establish new sufficient as well as necessary and sufficient conditions for robust Lipschitzian stability of parametric constraint systems with evaluating the exact Lipschitzian bounds. Most results are obtained for the class of Asplund spaces, which particularly includes all reflexive spaces, although some important characteristics are given in the general Banach space setting.

## Keywords

Variational analysis generalized differentiation parametric constraint systems Lipschitzian stability coderivatives Asplund spaces## Preview

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