Expected Residual Minimization Method for a Class of Stochastic Tensor Variational Inequalities

doi:10.1007/s40305-024-00569-6

Journal of the Operations Research Society of China ›› 2026, Vol. 14 ›› Issue (2): 565-590.doi: 10.1007/s40305-024-00569-6

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Expected Residual Minimization Method for a Class of Stochastic Tensor Variational Inequalities

Jian-Xun Liu¹, Zhao-Feng Lan², Sheng-Jie Li³

1 School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, Guangxi, China;
2 School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, Guangxi, China;
3 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2023-08-15 Revised:2024-02-08 Online:2026-06-30 Published:2026-07-06
Contact: Sheng-Jie Li E-mail:lisj@cqu.edu.cn
Supported by:
The research was partially supported by Guangxi Natural Science Foundation (No. 2024GXNSFBA010345), Guangxi Science and Technology Plan Project (No. guikeAD22035021), the Basic Ability Enhancement Program for Young and Middle-aged Teachers of Guangxi (No. 2022KY0163), the National Natural Science Foundation of China (No.12261008), the XiangsihuYoung Scholars and Innovative Research Team of GXMZU (No. 2022GXUNXSHQN02).

Abstract

Abstract: This paper considers the expected residual minimization (ERM) formulation for a class of stochastic tensor variational inequalities (STVI) where the involved set contains 0. Initially, we derive some theoretical results regarding the H-eigenvalues of tensors and formulate a class of stochastic multi-person nonoperative games as an STVI. Subsequently, we transform the STVI into an ERM problem by using the regularized gap function and explore the properties of the object function. Furthermore, we use the quasi-Monte Carlo method to address the ERM problem and conduct convergence analysis. Ultimately, we conduct numerical experiments to validate our theoretical findings.

Key words: Stochastic tensor variational inequalities, ERM formulation, H-eigenvalues of tensors, Convergence analysis

CLC Number:

90C15
90C33

Jian-Xun Liu, Zhao-Feng Lan, Sheng-Jie Li. Expected Residual Minimization Method for a Class of Stochastic Tensor Variational Inequalities[J]. Journal of the Operations Research Society of China, 2026, 14(2): 565-590.

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URL: https://www.jorsc.shu.edu.cn/EN/10.1007/s40305-024-00569-6

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Expected Residual Minimization Method for a Class of Stochastic Tensor Variational Inequalities

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