This paper considers a class of two-stage stochastic linear variational inequality problems whose first stage problems are stochastic linear box-constrained variational inequality problems and second stage problems are stochastic linear complementary problems having a unique solution. We first give conditions for the existence of solutions to both the original problem and its perturbed problems. Next we derive quantitative stability assertions of this two-stage stochastic problem under total variation metrics via the corresponding residual function. Moreover, we study the discrete approximation problem. The convergence and the exponential rate of convergence of optimal solution sets are obtained under moderate assumptions respectively. Finally, through solving a non-cooperative game in which each player’s problem is a parameterized two-stage stochastic program, we numerically illustrate our theoretical results.

中文翻译：

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一类两阶段随机线性变分不等式问题的定量分析

本文考虑一类两阶段随机线性变分不等式问题，其第一阶段问题是随机线性箱约束变分不等式问题，第二阶段是随机线性互补问题，具有独特的解决方案。我们首先给出解决原始问题及其摄动问题的解决方案的条件。接下来，我们通过相应的残差函数，得出在总变化量度下该两阶段随机问题的定量稳定性断言。此外，我们研究了离散逼近问题。最优解集的收敛性和指数收敛率分别在中等假设下获得。最后，