Fenchel–Rockafellar Duality

Abstract

Of central importance in convex analysis are conditions guaranteeing that the conjugate of a sum is the infimal convolution of the conjugates. The main result in this direction is a theorem due to Attouch and Br9zis. In turn, it gives rise to the Fenchel–Rockafellar duality framework for convex optimization problems. The applications we discuss include von Neumann’s minimax theorem as well as several results on the closure of the sum of linear subspaces.