Journal of Convex Analysis 12 (2005), No. 2, 255--265
Copyright Heldermann Verlag 2005
Subdifferential Representation of Convex Functions: Refinements and Applications
Joël Benoist
Faculté des Sciences, LACO, URA CNRS 1586, 123 av. Albert Thomas, Université de Limoges, France
benoist@unilim.fr
Aris Daniilidis
Dep. de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
arisd@mat.uab.es
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.
Keywords: Convex function, subdifferential, epi-pointed function, cusco mapping, strongly exposed point.
MSC: 52A41, 46B22, 26E25
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