Directional Hölder Metric Regularity

This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder/Lipschitz metric regularity is...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 171; no. 3; pp. 785 - 819
Main Authors: Van Ngai, Huynh, Tron, Nguyen Huu, Théra, Michel
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2016
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Control theory
Engineering
Mathematical functions
Mathematical models
Mathematics
Mathematics and Statistics
Neighborhoods
Operations Research/Decision Theory
Optimization
Regularity
Sensitivity analysis
Sheds
Slopes
Stability
Stability analysis
Studies
Theory of Computation
Fréchet subdifferential
58C06
Ekeland variational principle
Slope
Hadamard directional differentiability
90C30
49J53
49J52
Generalized equation
Asplund spaces
Metric regularity
Hölder metric regularity
54C60
47H04
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Hölder/Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-015-0797-6