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 
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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/