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Sensitivity Analysis for Variational Systems

  • B. S. Mordukhovich
Chapter
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)

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.

Key words

Variational systems Lipschitzian stability variational analysis generalized differentiation 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • B. S. Mordukhovich
    • 1
  1. 1.Dept. of MathematicsWayne State UniversityDetroitUSA

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