Geodesic
A Complete Characterization of the Subdifferential Set of the Supremum of an Arbitrary Family of Convex Functions
Journal of convex analysis, Tome 15 (2008) no. 4, pp. 831-858

Voir la notice de l'article provenant de la source Heldermann Verlag

Starting with some analysis of the support function of an arbitrary set, we obtain a formula for the subdifferential set of the supremum function of an arbitrary (possibly infinite) family of proper convex functions at each point of its effective domain, not necessarily at a continuity point. In this sense, our formula constitutes an extension of Theorem A of M. Volle ["Sous-différentiel d'une enveloppe supérieure de fonctions convexes", Comptes Rendus Acad. Sci. Paris I 317 (1993) 845-849], and also allows us to derive a generalization of a result A. Broensted ["On the subdifferential of the supremum of two convex functions", Math. Scand. 31 (1972) 225-230]. Our approach is based on a linearization via the Fenchel conjugate.
Classification : 52A41, 90C25, 15A39
Mots-clés : Subdifferential set, support and supremum functions, convex analysis 
@article{JCA_2008_15_4_JCA_2008_15_4_a9,
     author = {A. Hantoute and M. A. L\'opez},
     title = {A {Complete} {Characterization} of the {Subdifferential} {Set} of the {Supremum} of an {Arbitrary} {Family} of {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {831--858},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a9/}
}
TY  - JOUR
AU  - A. Hantoute
AU  - M. A. López
TI  - A Complete Characterization of the Subdifferential Set of the Supremum of an Arbitrary Family of Convex Functions
JO  - Journal of convex analysis
PY  - 2008
SP  - 831
EP  - 858
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a9/
ID  - JCA_2008_15_4_JCA_2008_15_4_a9
ER  - 
%0 Journal Article
%A A. Hantoute
%A M. A. López
%T A Complete Characterization of the Subdifferential Set of the Supremum of an Arbitrary Family of Convex Functions
%J Journal of convex analysis
%D 2008
%P 831-858
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a9/
%F JCA_2008_15_4_JCA_2008_15_4_a9
A. Hantoute; M. A. López. A Complete Characterization of the Subdifferential Set of the Supremum of an Arbitrary Family of Convex Functions. Journal of convex analysis, Tome 15 (2008) no. 4, pp. 831-858. http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a9/