On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems

Abstract

We study continuous quadratic submodular minimization with bounds and propose a polynomially sized semidefinite relaxation, which is provably tight for dimension $n \le 3$ and empirically tight for larger $n$. We apply the relaxation to two moment problems arising in distributionally robust optimization and the computation of covariance bounds. Accordingly, this research advances the ongoing study of continuous submodular minimization and opens new application areas therein.