  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.
