Strong duality in infinite convex optimization

Abstract

We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums of functions. Unlike the classical Haar duality scheme, these dual problems provide zero duality gap and are solvable under the standard Slater condition. Then we derive general optimality conditions/multiplier rules by applying subdifferential rules for infinite sums established in [13].