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Issue ESAIM: PROC
Volume 20, 2007
RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005
Page(s) 157 - 169
DOI 10.1051/proc:072015
Published online 13 October 2007

ESAIM: Proc., 2007, Vol. 20, pp. 157-169
DOI: 10.1051/proc:072015

Bounded convergence of convex composed functions

M. Laghdir, R. Benabbou and N. Benkenza

Département de Mathématiques et Informatique, Faculté des Sciences. B.P 20, El-Jadida, Maroc


(Published online: 13 October 2007)

Abstract
In this paper we establish conditions that guarantee, in the setting of normed vector spaces, the bounded convergence (also called Attouch-Wets convergence) of convex composed functions. We also provide applications to the convergence of multipliers of families of constrained convex optimization and to the continuity of inf-convolution and level sum operations.


Résumé
Dans ce papier nous établissons les conditions garantissant, dans le cadre des espaces vectoriels normés, la convergence des fonctions convexes composées au sens d'Attouch-Wets. Nous appliquons ce résultat de stabilité pour étudier la continuité des multiplicateurs de Lagrange associés à une famille de problèmes de minimisation convexes avec contraintes et aussi la continuité des opérations inf-convolution et level sum.


Mathematics Subject Classification. 90C25, 49A50, 52A50

Key words: bounded convergence, Attouch-Wets topology, bounded Hausdorff topology, convex composed functions, constraint qualifications, preorder.


© EDP Sciences, ESAIM 2007


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