A Two-Stage Moment Robust Optimization Model and its Solution Using Decomposition∗

Moment robust optimization models formulate a stochastic problem with an uncertain probability distribution of parameters described by its moments. In this paper we study a two-stage stochastic convex programming model using moments to define the probability ambiguity set for the objective function coefficients in both stages. A decomposition based algorithm is given. We show that this two-stage model can be solved to any precision in polynomial time. We consider a special case where the probability ambiguity sets are described by the exact information of the first two moments and the convex functions are piece-wise linear utility functions. A two-stage stochastic semidefinite programming formulation is given of this problem and we provide computational results on the performance of this problem using a portfolio optimization application. Results show that the two stage modeling is effective when forecasting models have predictive power.