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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| Vydané v: | Nonlinear analysis Ročník 73; číslo 7; s. 2271 - 2282 |
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| Médium: | Journal Article |
| Jazyk: | English |
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01.10.2010
Elsevier |
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| ISSN: | 0362-546X, 1873-5215 |
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| Abstract | 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]. |
|---|---|
| AbstractList | 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] and [12]. 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]. |
| Author | Nam, Nguyen Mau |
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| Cites_doi | 10.1016/0021-8928(76)90136-2 10.2307/2154544 10.1070/RM2000v055n03ABEH000292 10.1137/06067438 10.1016/j.na.2008.11.089 10.1137/090766413 10.1137/060665609 10.1016/j.na.2007.12.025 10.1137/S1052623495284029 10.1007/s10492-007-0028-z |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities |
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