Expected Residual Minimization Method for Stochastic Tensor Variational Inequalities  

作　　者：Tong-Tong Shang Guo-Ji Tang 

机构地区：[1]School of Mathematics and Statistics,Guizhou University,Guiyang,550025,Guizhou,China [2]School of Mathematics and Physics,Guangxi Minzu University,Nanning,530006,Guangxi,China [3]School of Mathematics and Physics,Center for Applied Mathematics of Guangxi,Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis,Guangxi Minzu University,Nanning,530006,Guangxi,China

出　　处：《Journal of the Operations Research Society of China》2024年第4期1048-1071,共24页中国运筹学会会刊(英文)

基　　金：supported by the National Natural Science Foundation of China(No.11961006);Guangxi Natural Science Foundation(No.2020GXNSFAA159100).

摘　　要：The goal of this paper is to introduce and investigate a model called the stochastic tensor variational inequality(denoted by STVI),which is a natural extension of the stochastic linear complementarity problem and the stochastic affine variational inequality.Firstly,the STVI is transformed into an expected residual minimization(ERM)problem involved the regularized gap function.Then,the properties of the ERM problem are investigated.Finally,a discrete approximation of ERM problem is obtained by quasi-Monte Carlo method.The convergence of optimal solutions and stationary points of the approximation problem are analyzed as well.

关 键 词：Stochastic tensor variational inequality Strongly monotone tensor Level set Convergence 

分 类 号：O17[理学—数学]