ABSTRACT

This paper focus on the quantitative stability of a class of two-stage stochastic linear variational inequality problems whose second stage problems are stochastic linear complementarity problems with fixed recourse matrix. Firstly, we discuss the existence of solutions to this two-stage stochastic problems and its perturbed problems. Then, by using the corresponding residual function, we derive the quantitative stability of this two-stage stochastic problem under Fortet-Mourier metric. Finally, we study the sample average approximation problem, and obtain the convergence of optimal solution sets under moderate assumptions.

中文翻译：

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具有固定追索权的两阶段随机线性变分不等式问题的定量稳定性

摘要

本文重点研究一类两阶段随机线性变分不等式问题的定量稳定性，其第二阶段问题是具有固定追索矩阵的随机线性互补问题。首先，我们讨论了这个两阶段随机问题及其扰动问题的解的存在性。然后，通过使用相应的残差函数，我们得出了这个两阶段随机问题在 Fortet-Mourier 度量下的定量稳定性。最后，我们研究了样本平均逼近问题，得到了适度假设下最优解集的收敛性。