Lipschitzian Stability of Parametric Constraint Systems in Infinite Dimensions
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.
KeywordsVariational analysis generalized differentiation parametric constraint systems Lipschitzian stability coderivatives Asplund spaces
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- Ioffe, A.D. (2000), Codirectional compactness, metric regularity and subdifferential calculus, in Théra, M. (ed.), Experimental, Constructive, and Nonlinear Analysis, CMS Conference Proceedings, Vol. 27, pp. 123–164, American Mathematical Society, Providence, Phode Island.Google Scholar
- Fabian, M. and Mordukhovich, B.S. (2001), Sequential normal compactness versus topological normal compactness in variational analysis, to appear in Nonlinear Analysis.Google Scholar
- Levy, A.B. and Mordukhovich, B.S. (2002), Coderivatives in parametric optimization, to appear in Mathematical Programming.Google Scholar
- Mordukhovich, B.S. (2001), The extremal principle and its applications to optimization and economics, In Optimization and Related Topics (Rubinov, A. and Glover, B., eds.), Applied Optimization Volumes 47, pp. 323–370, Kluwer, Dordrecht.Google Scholar
- Mordukhovich, B.S. (2002), Coderivative analysis of variational systems, to appear in Journal of Global Optimization.Google Scholar
- Mordukhovich, B.S. and Wang, Y. (2002), Restrictive metric regularity and generalized differential calculus in Banach spaces, preprint.Google Scholar
- Ye, J.J. and Zhu, Q.J. (2001), Multiobjective optimization problems with variational inequality constraints, to appear in Mathematical Programming.Google Scholar