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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Vydáno v:	Journal of optimization theory and applications Ročník 171; číslo 3; s. 785 - 819
Hlavní autoři:	Van Ngai, Huynh, Tron, Nguyen Huu, Théra, Michel
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.12.2016 Springer Nature B.V
Témata:	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
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Abstract	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.
AbstractList	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. This paper sheds new light on regularity of multifunctions through various characterizations of directional Holder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Holder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Holder/Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.
Author	Théra, Michel Tron, Nguyen Huu Van Ngai, Huynh
Author_xml	– sequence: 1 givenname: Huynh surname: Van Ngai fullname: Van Ngai, Huynh organization: Department of Mathematics, University of Quy Nhon – sequence: 2 givenname: Nguyen Huu surname: Tron fullname: Tron, Nguyen Huu organization: Department of Mathematics, University of Quy Nhon – sequence: 3 givenname: Michel surname: Théra fullname: Théra, Michel email: michel.thera@unilim.fr, m.thera@federation.edu.au organization: Laboratoire XLIM, Université de Limoges, Federation University Australia
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Snippet	This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder/Lipschitz metric regularity, which are based... This paper sheds new light on regularity of multifunctions through various characterizations of directional Holder/Lipschitz metric regularity, which are based...
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SubjectTerms	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
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Title	Directional Hölder Metric Regularity
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