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Stability of Implicit Multifunctions in Banach Spaces

Author

Listed:
  • N. Q. Huy

    (Hanoi Pedagogical University No. 2)

  • D. S. Kim

    (Pukyong National University)

  • K. V. Ninh

    (Hanoi Pedagogical University No. 2)

Abstract

This paper is devoted to present new sufficient conditions for both the metric regularity in the Robinson’s sense and the Lipschitz-like property in the Aubin’s sense of implicit multifunctions in general Banach spaces. The basic tools of our analysis involve the Clarke subdifferential, the Clarke coderivative of set-valued mappings, and the Ekeland variational principle. The metric regularity of implicit multifunction is compared with the Lipschitz-like property.

Suggested Citation

  • N. Q. Huy & D. S. Kim & K. V. Ninh, 2012. "Stability of Implicit Multifunctions in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 558-571, November.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0058-x
    DOI: 10.1007/s10957-012-0058-x
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    References listed on IDEAS

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    1. Jean-Pierre Aubin, 1984. "Lipschitz Behavior of Solutions to Convex Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 87-111, February.
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    Cited by:

    1. Thai Doan Chuong & Do Sang Kim, 2016. "Hölder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 596-611, May.
    2. Thai Doan Chuong, 2019. "Stability of Implicit Multifunctions via Point-Based Criteria and Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 920-943, December.

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