A semi-infinite programming approach to two-stage stochastic linear programs with high-order moment constraints

We consider distributionally robust two-stage stochastic linear optimization problems with higher-order (say and even possibly irrational) moment constraints in their ambiguity sets. We suggest to solve the dual form of the problem by a semi-infinite programming approach, which deals with a much simpler reformulation than the conic optimization approach. Some preliminary numerical results are reported.