Issue |
ESAIM: Proc.
Volume 13, 2003
Proceedings of 2003 MODE-SMAI Conference
|
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Page(s) | 1 - 17 | |
DOI | https://doi.org/10.1051/proc:2003004 | |
Published online | 05 December 2003 |
A survey on error bounds for lower semicontinuous functions
UMR CNRS MIP, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse cedex, France.
Corresponding author: aze@mip.ups-tlse.fr
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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