Geodesic
Subdifferential Representation of Convex Functions: Refinements and Applications
Journal of convex analysis, Tome 12 (2005) no. 2, pp. 255-265.

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

Every lower semicontinuous convex function can be represented through its subdifferential by means of an "integration" formula introduced by R. T. Rockafellar [Pacific J. Math. 33 (1970) 209--216]. We show that in Banach spaces with the Radon-Nikodym property this formula can be significantly refined under a standard coercivity assumption. This yields an interesting application to the convexification of lower semicontinuous functions.
Classification : 52A41, 46B22, 26E25
Mots-clés : Convex function, subdifferential, epi-pointed function, cusco mapping, strongly exposed point 
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J. Benoist; A. Daniilidis. Subdifferential Representation of Convex Functions: Refinements and Applications. Journal of convex analysis, Tome 12 (2005) no. 2, pp. 255-265. http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a0/