Stability and sensitivity analysis of stochastic programs with second order dominance constraints

Abstract

In this paper we present stability and sensitivity analysis of a stochastic optimizationproblem with stochastic second order dominance constraints. We consider perturbation of theunderlying probability measure in the space of regular measures equipped with pseudometricdiscrepancy distance ( [30]). By exploiting a result on error bound in semi-infinite programmingdue to Gugat [13], we show under the Slater constraint qualification that the optimal valuefunction is Lipschitz continuous and the optimal solution set mapping is upper semicontinuouswith 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.