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.

在本文中，我们考虑了一类随机非线性互补问题（SNCP）的样本平均近似（SAA）方法，并研究了相应的收敛特性。我们首先研究当第一阶段问题是连续可微的并且第二阶段问题是局部 Lipschitz 连续问题时，两阶段 SNCP 的 SAA 对应项的收敛性。之后，我们将收敛结果扩展到一类多级 SNCP，其每一级的决策变量仅受相邻级的决策变量的影响。最后，给出了一些初步的数值试验来说明收敛结果。