A weighted expected residual minimization method with sample average approximation for stochastic vector variational inequalities

In this paper, we propose a novel solution approach for a specific class of stochastic vector variational inequalities (SVVI). Our method adopts a weighted expected residual framework that includes a regularized gap function, which incorporates convex combinations of residuals derived from both the least absolute deviation (LAD) and least squares (LS) methods. We conduct a detailed analysis of the core properties of the resulting weighted expected residual minimization (WERM) problem, including differentiability, level set boundedness, global error bounds, and solution robustness. To enhance its practical utility, we further develop a sample average approximation (SAA) technique for solving the WERM problem, and provide a comprehensive convergence analysis of this approximation scheme. Finally, a series of numerical experiments are carried out to validate the theoretical results of this study and demonstrate the effectiveness of the proposed approach.