Robust two-stage stochastic linear programs with moment constraints

We consider the two-stage stochastic linear programming model, in which the recourse function is a worst case expected value over a set of probabilistic distributions. These distributions share the same first- and second-order moments. By using duality of semi-infinite programming and assuming knowledge on extreme points of the dual polyhedron of the constraints, we show that a deterministic equivalence of the two-stage problem is a second-order cone optimization problem. Numerical examples are presented to show non-conservativeness and computational advantage of this approach.