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

Jian-Xun Liu (), Zhao-Feng Lan () and Zheng-Hai Huang ()
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Jian-Xun Liu: Guangxi Minzu University
Zhao-Feng Lan: Guangxi Minzu University
Zheng-Hai Huang: Tianjin University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 11, 23 pages

Abstract: 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.

Keywords: Stochastic tensor vector variational inequality; Expected residual minimization formulation; Positive definite tensors; Sample average approximation; Convergence analysis; 90C15; 90C33 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02813-2

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