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Directional Hölder Metric Regularity

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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.

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Acknowledgments

Many thanks to the referees for their helpful comments and suggestions which have led to an improved paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Quy Nhon, 170 An Duong Vuong, Quy Nhon, Vietnam

    Huynh Van Ngai & Nguyen Huu Tron

  2. Laboratoire XLIM, Université de Limoges, Limoges, France

    Michel Théra

  3. Federation University Australia, Ballarat, Australia

    Michel Théra

Authors
  1. Huynh Van Ngai
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  2. Nguyen Huu Tron
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  3. Michel Théra
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Correspondence to Michel Théra.

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Research partially supported by Ministerio de Economıa y Competitividad under Grant MTM2011-29064-C03(03), by LIA “FormathVietnam” and by NAFOSTED.

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Van Ngai, H., Tron, N.H. & Théra, M. Directional Hölder Metric Regularity. J Optim Theory Appl 171, 785–819 (2016). https://doi.org/10.1007/s10957-015-0797-6

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