Distributionally Robust Optimization with Moment Ambiguity Sets

Abstract

This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with equivalent moment conic constraints. Under some general assumptions, we prove the DRO is equivalent to a linear optimization problem with moment and psd polynomial cones. A Moment-SOS relaxation method is proposed to solve it. Its asymptotic and finite convergence are shown under certain assumptions. Numerical examples are presented to show how to solve DRO problems.

Distributionally robust sparse portfolio optimization model under satisfaction criterion

“…In distributionally robust optimization, optimal solutions are evaluated under the worst-case expectation with respect to a set of probability distributions of uncertain parameters. The ambiguity set is used to describe the uncertainty of the parameter and is often moment-based, see Zymler et al [38], Hanasusanto et al [16] and Nie et al [25]. Moment-based ambiguity sets, which contain probability distributions of asset returns whose moments satisfy certain conditions, are commonly adopted in distributionally robust portfolio optimization.…”