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Directional Hölder Metric Regularity

Author

Listed:
  • Huynh Ngai

    (University of Quy Nhon)

  • Nguyen Huu Tron

    (University of Quy Nhon)

  • Michel Théra

    (Université de Limoges
    Federation University Australia)

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.

Suggested Citation

  • Huynh Ngai & Nguyen Huu Tron & Michel Théra, 2016. "Directional Hölder Metric Regularity," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 785-819, December.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-015-0797-6
    DOI: 10.1007/s10957-015-0797-6
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    References listed on IDEAS

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    1. Marian J. Fabian & René Henrion & Alexander Y. Kruger & Jiří V. Outrata, 2012. "About error bounds in metric spaces," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 33-38, Springer.
    2. Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), 2012. "Operations Research Proceedings 2011," Operations Research Proceedings, Springer, edition 127, number 978-3-642-29210-1, May.
    3. Huynh Van Ngai & Phan Nhat Tinh, 2015. "Metric Subregularity of Multifunctions: First and Second Order Infinitesimal Characterizations," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 703-724, March.
    4. Aram V. Arutyunov & Alexey F. Izmailov, 2006. "Directional Stability Theorem and Directional Metric Regularity," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 526-543, August.
    5. Boris Mordukhovich & Wei Ouyang, 2015. "Higher-order metric subregularity and its applications," Journal of Global Optimization, Springer, vol. 63(4), pages 777-795, December.
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