Discrete Approximation Scheme in Distributionally Robust Optimization

Discrete approximation which is the prevailing scheme in stochastic programming in the past decade has been extended to distributionally robust optimization (DRO) recently. In this paper we conduct rigorous quantitative stability analysis of discrete approximation schemes for DRO, which measures the approximation error in terms of discretization sample size. For the ambiguity set defined through … Read more

Quantitative Stability Analysis for Minimax Distributionally Robust RiskOptimization

This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage. We carry out stability analysis by looking into variations of the ambiguity set under the Wasserstein metric, decision spaces at both stages and the support … Read more

Quantitative Stability Analysis for Distributionally Robust Optimization With Moment Constraints

In this paper we consider a broad class of distributionally robust optimization (DRO for short) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is de ned through parametric moment conditions with generic cone constraints. Under some moderate conditions including Slater type conditions of cone constrained moment … Read more

Quantitative Stability Analysis of Stochastic Quasi-Variational Inequality Problems and Applications

We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is de ned over the solution set of a parametric stochastic cone system. We investigate the impact of variation of the probability measure and the parameter on the solution of the SQVIP. By reformulating the SQVIP as a natural equation … Read more