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

被引：23

作者：

Nam, Nguyen Mau ^{[1
]}

机构：

[1] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 07期

关键词：

Variational analysis and optimization; Reflexive Banach spaces; Polyhedral sets; Parametric variational inequalities; Lipschitzian stability; Generalized differentiation; Coderivatives; METRIC REGULARITY; CONSTRAINTS; CALCULUS; SYSTEMS;

D O I：

10.1016/j.na.2010.06.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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]. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2271 / 2282

页数：12

共 44 条

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Ban, Liqun
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Song, Wen
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (02) : 441 - 461
[2] Lipschitzian stability of parametric variational inequalities over perturbed polyhedral convex sets
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OPTIMIZATION LETTERS, 2012, 6 (04) : 749 - 762
[3] Metric regularity and Lipschitzian stability of parametric variational systems
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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) : 1149 - 1170
[4] Lipschitzian stability of parametric variational inequalities over perturbed polyhedral convex sets
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Optimization Letters, 2012, 6 : 749 - 762
[5] Nonlinear Perturbations of Polyhedral Normal Cone Mappings and Affine Variational Inequalities
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[6] SECOND-ORDER ANALYSIS OF POLYHEDRAL SYSTEMS IN FINITE AND INFINITE DIMENSIONS WITH APPLICATIONS TO ROBUST STABILITY OF VARIATIONAL INEQUALITIES
Henrion, Rene
Mordukhovich, Boris S.
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SIAM JOURNAL ON OPTIMIZATION, 2010, 20 (05) : 2199 - 2227
[7] Exact Formulae for Coderivatives of Normal Cone Mappings to Perturbed Polyhedral Convex Sets
Huy, N. Q.
Yao, J. -C.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2013, 157 (01) : 25 - 43
[8] Linearly perturbed generalized polyhedral normal cone mappings and applications
Ban, Liqun
Song, Wen
OPTIMIZATION, 2016, 65 (01) : 9 - 34
[9] Lipschitzian stability of parametric constraint systems in infinite dimensions
Mordukhovich, BS
GENERALIZED CONVEXITY, GENERALIZED MONOTONICITY AND APPLICATIONS, 2005, 77 : 39 - 59
[10] Coderivative calculus and robust Lipschitzian stability of variational systems
Mordukhovich, Boris S.
JOURNAL OF CONVEX ANALYSIS, 2006, 13 (3-4) : 799 - 822

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