Estimates of the duality gap for large-scale separable nonconvex optimization problems

We derive some estimates of the duality gap for separable constrained optimization problems involving nonconvex, possibly discontinuous, objective functions, and nonconvex, possibly discrete, constraint sets. The main result is that as the number of separable terms increases to infinity the duality gap as a fraction of the optimal cost decreases to zero. The analysis is related to the one of Aubin and Ekeland [1], and is based on the Shapley-Folkman theorem. Our assumptions are different and our estimates are sharper and more convenient for integer programming problems.