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Characterizations of error bounds for lower semicontinuous functions on metric spaces

Dominique Az (aze***at***mip.ups-tlse.fr)
Jean-Nol Corvellec (corvellec***at***univ-perp.fr)

Abstract: By using a variational method based on Ekeland's principle, we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces, and the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces.

Keywords: error bounds, metric regularity, variational methods

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization

Citation: ESAIM Control, Optimization and Calculus of Variations, Vol. 10 (2004) 409-425


Entry Submitted: 05/12/2003
Entry Accepted: 05/12/2003
Entry Last Modified: 07/13/2004

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