Fenchel–Rockafellar theorem in infinite dimensions via generalized relative interiors

Abstract

In this paper we provide further studies of Fenchel duality theory in the general framework of locally convex topological vector (LCTV) spaces. We prove the validity of the Fenchel strong duality under some qualification conditions via generalized relative interiors imposed on the epigraphs and the domains of the functions involved. Our results directly generalize the classical Fenchel–Rockafellar theorem on strong duality from finite dimensions to LCTV spaces.