Stability and Sensitivity Analysis of Stochastic Programs with Second Order Dominance Constraints

In this paper we present stability and sensitivity analysis of a stochastic optimization problem with stochastic second order dominance constraints. We consider perturbation of the underlying probability measure in the space of regular measures equipped with pseudometric discrepancy distance ( [30]). By exploiting a result on error bound in semi-infinite programming due to Gugat [13], we show under the Slater constraint qualification that the optimal value function is Lipschitz continuous and the optimal solution set mapping is upper semicontinuous with respect to the perturbation of the probability measure. In particular, we consider the case when the probability measure is approximated by empirical probability measure and show the exponential rate of convergence of optimal solution obtained from solving the approximation problem. The analysis is extended to the stationary points when the objective function is nonconvex.