Abstract
The paper mostly concerns applications of the generalized differentiation theory in variational analysis to Lipschitzian stability and metric regularity of variational systems in infinite-dimensional spaces. The main tools of our analysis involve coderivatives of set-valued mappings that turn out to be proper extensions of the adjoint derivative operator to nonsmooth and set-valued mappings. The involved coderivatives allow us to give complete dual characterizations of certain fundamental properties in variational analysis and optimization related to Lipschitzian stability and metric regularity. Based on these characterizations and extended coderivative calculus, we obtain efficient conditions for Lipschitzian stability of variational systems governed by parametric generalized equations and their specifications.
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Mordukhovich, B.S. Coderivative Analysis of Variational Systems. Journal of Global Optimization 28, 347–362 (2004). https://doi.org/10.1023/B:JOGO.0000026454.56343.b9
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DOI: https://doi.org/10.1023/B:JOGO.0000026454.56343.b9