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Characterizations of error bounds for lower semicontinuousfunctions on metric spaces

Published online by Cambridge University Press:  15 June 2004

Dominique Azé  and
Jean-Noël Corvellec
Dominique Azé
Affiliation:
UMR CNRS MIP, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France; aze@mip.ups-tlse.fr.
Jean-Noël Corvellec
Affiliation:
Laboratoire MANO, Université de Perpignan, 52 avenue de Villeneuve, 66860 Perpignan Cedex, France.
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Abstract

Refining the variational method introduced in Azé et al. [Nonlinear Anal. 49 (2002) 643-670], 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 (refining the abstract part of Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization of the local metric regularity of closed-graph multifunctions between complete metric spaces.

Keywords

Error boundsstrong slopevariational principlemetric regularity.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 3 , July 2004 , pp. 409 - 425
Copyright
© EDP Sciences, SMAI, 2004

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