Directional Hölder Metric Regularity

Huynh Ngai (), Nguyen Huu Tron () and Michel Théra ()
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Huynh Ngai: University of Quy Nhon
Nguyen Huu Tron: University of Quy Nhon
Michel Théra: Université de Limoges

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 3, No 3, 785-819

Abstract: 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.

Keywords: Slope; Metric regularity; Hölder metric regularity; Generalized equation; Fréchet subdifferential; Asplund spaces; Ekeland variational principle; Hadamard directional differentiability; 49J52; 49J53; 58C06; 47H04; 54C60; 90C30 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0797-6

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