Journal of Convex Analysis 12 (2005), No. 2, 255--265
Copyright Heldermann Verlag 2005
Subdifferential Representation of Convex Functions: Refinements and Applications
Faculté des Sciences, LACO, URA CNRS 1586, 123 av. Albert Thomas, Université de Limoges, France
Dep. de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
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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