In this paper, we consider the sample average approximation (SAA) approach for a class of stochastic nonlinear complementarity problems (SNCPs) and study the corresponding convergence properties. We first investigate the convergence of the SAA counterparts of two-stage SNCPs when the first-stage problem is continuously differentiable and the second-stage problem is locally Lipschitz continuous. After that, we extend the convergence results to a class of multistage SNCPs whose decision variable of each stage is influenced only by the decision variables of adjacent stages. Finally, some preliminary numerical tests are presented to illustrate the convergence results.

中文翻译：

---

一类随机非线性互补问题的样本平均逼近的收敛性分析：从两阶段到多阶段。

在本文中，我们考虑了一类随机非线性互补问题（SNCP）的样本平均逼近（SAA）方法，并研究了相应的收敛性。我们首先研究两阶段SNCP的SAA对应项的收敛性，其中第一阶段的问题是连续可微的，第二阶段的问题是局部Lipschitz连续的。之后，我们将收敛结果扩展到一类多级SNCP，其每个阶段的决策变量仅受相邻阶段的决策变量影响。最后，提出了一些初步的数值测试来说明收敛结果。