In this paper, a class of stochastic mathematical programs with probabilistic complementarity constraints is considered. We first investigate convergence properties of sample average approximation (SAA) approach to the corresponding chance constrained relaxed complementarity problem. Our discussion can be not only applied to the specific model in this paper, but also viewed as a supplementary for the SAA approach to general joint chance constrained problems. Furthermore, considering the uncertainty of the underlying probability distribution, a distributionally robust counterpart with a moment ambiguity set is proposed. The numerically tractable reformulation is derived. Finally, we use a production planing model to report some preliminary numerical results.

在本文中，考虑了一类具有概率互补约束的随机数学程序。我们首先研究样本平均近似（SAA）方法对相应机会约束松弛互补问题的收敛特性。我们的讨论不仅可以应用于本文中的特定模型，还可以视为 SAA 方法解决一般联合机会约束问题的补充。此外，考虑到潜在概率分布的不确定性，提出了具有矩模糊集的分布稳健对应物。导出了数值上易于处理的重构。最后，我们使用生产计划模型报告了一些初步的数值结果。