Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints

Abstract

We show that a separable polynomial program involving a box constraint enjoys a dual problem, that can be displayed in terms of sums of squares univariate polynomials. Under convexification and qualification conditions, we prove that a strong duality relation between the underlying separable polynomial problem and its corresponding dual holds, where the dual problem can be reformulated and solved as a semidefinite programming problem.