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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Jian-Xun Liu,
  • Zhao-Feng Lan,
  • Zheng-Hai Huang

摘要

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.