A stochastic mathematical program model with second-order cone complementarity constraints (SSOCMPCC) is introduced in this paper. It can be considered as a non-trivial extension of stochastic mathematical program with complementarity constraints, and could arise from a hard-to-handle class of bilivel second-order cone programming and inverse stochastic second-order cone programming. By introducing the Chen-Harker-Kanzow-Smale (CHKS) type function to replace the projection operator onto the second-order cone, a smoothing sample average approximation (SAA) method is proposed for solving the SSOCMPCC problem. It can be shown that with proper assumptions, as the sample size goes to infinity, any cluster point of global solutions of the smoothing SAA problem is a global solution of SSOCMPCC almost surely, and any cluster point of stationary points of the former problem is a C-stationary point of the latter problem almost surely. C-stationarity can be strengthened to M-stationarity with additional assumptions. Finally, we report a simple illustrative numerical test to demonstrate our theoretical results.

中文翻译：

---

具有二阶锥互补约束的随机数学程序的平滑SAA方法的收敛性分析

介绍了一种具有二阶锥互补约束的随机数学程序模型（SSOCMPCC）。它可以被认为是具有互补约束的随机数学程序的一个非平凡的扩展，并且可能是由一类难于处理的bilivel二阶锥规划和逆随机二阶锥规划引起的。通过引入Chen-Harker-Kanzow-Smale（CHKS）类型函数将投影算子替换到二阶圆锥上，提出了一种平滑样本平均逼近（SAA）方法来解决SSOCMPCC问题。可以证明，只要有适当的假设，当样本量达到无穷大时，平滑SAA问题的全局解决方案的任何聚类点几乎肯定是SSOCMPCC的全局解决方案，前一个问题的平稳点的任何聚类点几乎肯定是后一个问题的C平稳点。可以通过其他假设将C平稳性增强为M平稳性。最后，我们报告了一个简单的说明性数值测试，以证明我们的理论结果。