Free access article

ESAIM: Proc., December 2003, Vol. 13, pp. 1-17
DOI: 10.1051/proc:2003004

A survey on error bounds for lower semicontinuous functions

D. Azé

UMR CNRS MIP, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse cedex, France.

aze@mip.ups-tlse.fr

Abstract
We survey ancient and recent results on global error bounds for the distance to a sublevel set of a lower semicontinuous function defined on a complete metric space. We emphasize the case of a recent characterization of this property which appeared in [CITE]. We also review the convex case and show how the known result on sufficient condition for a global error bound can be derived from the quoted characterization.

Résumé
Nous revenons sur d'anciens et nouveaux résultats de borne d'erreur pour la distance à un ensemble de sous-niveau d'une fonction semi-continue inférieurement définie sur un espace métrique complet. Nous soulignons en particulier la caractérisation récente de cette propriété apparue dans [CITE]. On revient aussi sur le cas convexe, et on montre comment les résultats connus de conditions suffisantes pour une borne globale d'erreur découlent de la caractérisation citée.

Mathematics Subject Classification. 49J52, 90C26, 90C31

Key words: Error bounds, lower semicontinuous functions, subdifferential, metric regularity.


© EDP Sciences, ESAIM 2003

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