Fenchel duality in infinite-dimensional setting and its applications Original Research Article

We study Fenchel duality problems, in infinite-dimensional spaces, that involve the minimizing of a sum of two proper convex functions, where one of which is polyhedral. We use a constraint qualification with the notion of the strong quasi-interior of a convex set, and then deduce duality results and subgradient formula. As applications, we discuss the strong conical hull intersection property of convex sets. Finally, by using a duality result due to Rodriques and Simons, we establish several duality results for convex optimization over a finite intersection of closed convex sets.