A Fenchel-Rockafellar type duality theorem for maximization

Abstract

We prove that sup(f-h)(E) = sup(h*-f*)(E*), where f is a proper lower semi-continuous convex functional on a real locally convex space E, h: E → = [-∞, +∞] is an arbitrary-functional and, f*, h* are their convex conjugates respectively. When h = δG, the indicator of a bounded subset G of E, this yields a formula for sup f(G).