Nonlinear Perturbations of Polyhedral Normal Cone Mappings and Affine Variational Inequalities

This paper establishes an upper estimate for the Fréchet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the r...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 153; no. 1; pp. 98 - 122
Main Author: Qui, Nguyen Thanh
Format: Journal Article
Language:English
Published: Boston Springer US 01.04.2012
Springer Nature B.V
Subjects:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Engineering
Estimates
Inequalities
Inequality
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Operations Research/Decision Theory
Optimization
Perturbation methods
Studies
Theory of Computation
Vectors (mathematics)
Nonlinear perturbation
Mordukhovich coderivative
Estimate
Fréchet normal cone
Limiting normal cone
Polyhedral normal cone mapping
Parametric affine variational inequality
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper establishes an upper estimate for the Fréchet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the result leads to an upper estimate for values of the Mordukhovich coderivative of such mappings. On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-011-9937-9