Subdifferential Representation of Convex Functions: Refinements and Applications
Joël Benoist, Aris Daniilidis · Journal of convex analysis · 2005
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.