Expected Residual Minimization Method for Stochastic Tensor Variational Inequalities

doi:10.1007/s40305-022-00450-4

Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (4): 1048-1071.doi: 10.1007/s40305-022-00450-4

收稿日期:2022-03-31 修回日期:2022-09-18 出版日期:2024-12-30 发布日期:2024-12-12
通讯作者: Guo-Ji Tang, Tong-Tong Shang E-mail:guojvtang@126.com;ttshang0310@163.com

Expected Residual Minimization Method for Stochastic Tensor Variational Inequalities

Tong-Tong Shang^1,2, Guo-Ji Tang³

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

Received:2022-03-31 Revised:2022-09-18 Online:2024-12-30 Published:2024-12-12
Contact: Guo-Ji Tang, Tong-Tong Shang E-mail:guojvtang@126.com;ttshang0310@163.com
Supported by:
This work was partially supported by the National Natural Science Foundation of China (No.11961006) and Guangxi Natural Science Foundation (No. 2020GXNSFAA159100).

摘要/Abstract

Abstract: 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.

Key words: Stochastic tensor variational inequality, Strongly monotone tensor, Level set, Convergence

中图分类号:

. [J]. Journal of the Operations Research Society of China, 2024, 12(4): 1048-1071.

Tong-Tong Shang, Guo-Ji Tang. Expected Residual Minimization Method for Stochastic Tensor Variational Inequalities[J]. Journal of the Operations Research Society of China, 2024, 12(4): 1048-1071.

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Expected Residual Minimization Method for Stochastic Tensor Variational Inequalities

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