Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities

In this paper, we provide a comprehensive study of coderivative formulas for normal cone mappings. This allows us to derive necessary and sufficient conditions for the Lipschitzian stability of parametric variational inequalities in reflexive Banach spaces. Our development not only gives an answer t...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 73; no. 7; pp. 2271 - 2282
Main Author: Nam, Nguyen Mau
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.10.2010
Elsevier
Subjects:
Banach space
Calculus of variations and optimal control
Coderivatives
Complement
Exact sciences and technology
Functional analysis
Generalized differentiation
Global analysis, analysis on manifolds
Inequalities
Lipschitzian stability
Mapping
Mathematical analysis
Mathematics
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Parametric variational inequalities
Polyhedral sets
Reflexive Banach spaces
Sciences and techniques of general use
Stability
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Variational analysis and optimization
Variational analysis and optimization
Polyhedral sets
Parametric variational inequalities
49J52
49K40
Reflexive Banach spaces
58C20
Lipschitzian stability
Generalized differentiation
Coderivatives
Nonlinear analysis
Optimization method
Banach space
Variational inequality
Parametricvariational inequalities
Mathematical model
Numerical stability
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary:In this paper, we provide a comprehensive study of coderivative formulas for normal cone mappings. This allows us to derive necessary and sufficient conditions for the Lipschitzian stability of parametric variational inequalities in reflexive Banach spaces. Our development not only gives an answer to the open questions raised in Yao and Yen (2009)  [11], but also establishes generalizations and complements of the results given in Henrion et al. (2010)  [4] and Yao and Yen (2009)  [11,12].
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.06.007