Geodesic
Subdifferential Representation of Convex Functions: Refinements and Applications
Journal of convex analysis, Tome 12 (2005) no. 2, pp. 255-265 Cet article a éte moissonné depuis la source Heldermann Verlag

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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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     title = {Subdifferential {Representation} of {Convex} {Functions:} {Refinements} and {Applications}},
     journal = {Journal of convex analysis},
     pages = {255--265},
     year = {2005},
     volume = {12},
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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/