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Expected Residual Minimization Formulation for a Class of Stochastic Tensor Vector Variational Inequalities

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  • Jian-Xun Liu

    (Guangxi Minzu University
    Tianjin University)

  • Zhao-Feng Lan

    (Guangxi Minzu University)

  • Zheng-Hai Huang

    (Tianjin University)

Abstract

The goal of this paper is to introduce and consider a model called stochastic tensor vector variational inequality (STVVI), wherein the associated functions are defined by tensors. This model represents a natural generalization of the stochastic tensor variational inequality and constitutes a specific type of the stochastic vector variational inequality. Firstly, to obtain a reasonable solution for the STVVI, we consider the expected residual minimization (ERM) formulation for the STVVI. Then, based on the theory of structural tensors, we investigate some properties of the ERM problem. Finally, we derive a discrete approximation for the ERM problem by utilizing the sample average approximation method, and further demonstrate the convergence of both optimal solutions and stationary points of the approximation problem to that of the ERM problem.

Suggested Citation

  • Jian-Xun Liu & Zhao-Feng Lan & Zheng-Hai Huang, 2025. "Expected Residual Minimization Formulation for a Class of Stochastic Tensor Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-23, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02813-2
    DOI: 10.1007/s10957-025-02813-2
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    References listed on IDEAS

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    1. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    2. X.Q. Yang & J.C. Yao, 2002. "Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 407-417, November.
    3. Yong Zhao & Jin Zhang & Xinmin Yang & Gui-Hua Lin, 2017. "Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 545-566, November.
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