Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Convex function
  • subdifferential
  • epi-pointed function
  • cusco mapping
  • strongly exposed point

Mathematics Subject Classification

52A41, 46B22, 26E25

Suggested citation

J. Benoist, A. Daniilidis. “Subdifferential Representation of Convex Functions: Refinements and Applications.” Journal of Convex Analysis 12 (2005), No. 2, 255–265. https://doi.org/10.68381/jca12018

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2005. Rights now held by Banach Press.