Distributionally Robust Optimization with Polynomial Robust Constraints

This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving linear conic optimization with semidefinite constraints. When the DRO problem is SOS-convex, we show that it is equivalent to the linear conic relaxation and it can be solved by the Moment-SOS algorithm. For nonconvex cases, we also give concrete conditions such that the DRO can be solved globally. Numerical experiments are given to show the efficiency of the method.