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Implicit Multifunction Theorems in complete metric spaces

Van Ngai Huynh(nghiakhiem***at***yahoo.com)
Huu Tron Nguyen(huutronnguyen***at***yahoo.com)
Michel Thera(michel.thera***at***unilim.fr)

Abstract: 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.

Keywords: Error bound, Perturbation stability, Metric regularity, Implicit multifunction, Generalized equations

Category 1: Infinite Dimensional Optimization

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

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

Download: [PDF]

Entry Submitted: 06/12/2010
Entry Accepted: 06/12/2010
Entry Last Modified: 06/12/2010

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