Applicable Analysis ( IF 1.1 ) Pub Date : 2020-10-20 , DOI: 10.1080/00036811.2020.1836352 JianXun Liu 1 , ShengJie Li 1 , Jie Jiang 1
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:
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。