Mathematical programs with distributionally robust chance constraints: Statistical robustness, discretization and reformulation
研究了基于一般矩信息模糊集的分布鲁棒机会约束数学规划，从数据污染角度分析其统计鲁棒性，并提出了离散近似方法及重构公式，通过数值实验验证了有效性。
In this paper, we consider mathematical programs with distributionally robust chance constraints (MPDRCC), where the ambiguity set is given by the general moment information. From the contaminated data-driven viewpoint, we first study the qualitative statistical robustness of MPDRCC. Then, motivated by the computational tractability, we investigate the discrete approximation of MPDRCC. The corresponding convergence results of the optimal value and the optimal solution set of the discrete approximation problem are established. After that, a reformulation of the discrete approximation problem is presented under standard assumptions, which is applied to solve MPDRCC approximately according to the above convergence results. Finally, two applications are reported, and some numerical results show that the statistical robustness assertion and the discrete approximation scheme are practical and effective.