On Brøndsted–Rockafellar’s Theorem for convex lower semicontinuous epi-pointed functions in locally convex spaces

Abstract

In this work we give an extension of the Brondsted–Rockafellar Theorem, and some of its important consequences, to proper convex lower-semicontinuous epi-pointed functions defined in locally convex spaces. We use a new approach based on a simple variational principle, which also allows recovering the classical results in a natural way.