Implicit Multifunction Theorems in complete metric spaces

  • Van Ngai Huynh
  • Huu Tron Nguyen
  • Michel Thera
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization Tags , , , , Short URL: https://optimization-online.org/?p=11172

    In this paper, we establish some new characterizations of the metric regularity of implicit multifunctions in complete metric spaces by using the lower semicontinuous envelopes of the distance functions for set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.

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    Laboratory XLIM (UMR-CNRS 6172) 123, av. A. Thomas 87060 Limoges Cedex France

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