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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; [email protected].
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 givecharacterizationsof the existence of so-called global and local error bounds, for lowersemicontinuous functions defined on complete metric spaces. We thusprovide asystematic and synthetic approach to the subject, emphasizing the specialcaseof convex functions defined on arbitrary Banach spaces (refining theabstract partof Azé and Corvellec [SIAM J. Optim. 12 (2002) 913-927], and the characterization of the local metric regularityof 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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