Stochastic tensor complementarity problem: CVaR-ERM model and the convergence analysis of stationary points for its approximation problem

We focus on the expected residual minimization model with conditional value-at-risk constraints (CVaR-ERM Model) for solving the stochastic tensor complementarity problem (STCP). Our previous work (Zhang, Luo, Nguyen, in: J. Nonlinear Convex Anal. 26:61–76, 2025) explored the convergence of global optimal solutions of the approximate problem of the CVaR-ERM model. However, in some practical situations, both the proposed model and its approximate problem exhibit non-convex properties, which significantly raises the probability of obtaining stationary points during the solution process. Therefore, in this paper, we first formulate the approximate problem of the CVaR-ERM model using the smoothing method, the penalty function method, and the sample average approximation method. Subsequently, we prove the convergence of the stationary points of the proposed approximate problem.