CVaR Stochastic Programming Model for Monotone Stochastic Tensor Complementarity Problem by Using Its Penalized Sample Average Approximation Algorithm

This paper is concerned with the monotone stochastic tensor complementarity problem, where the expectation of the involved stochastic tensor is a strictly positive semi-definite tensor. At first, a new class of restricted nonlinear complementarity problem (NCP) function is defined by using the special structure of strictly semi-definite tensor. Then the conditional value at risk stochastic programming (CVaR-SP) model of monotone stochastic tensor complementarity problem (STCP) is established by taking the minimum value of the stochastic residual defined by the modified restricted NCP function as objective function, the nonnegativity of the variable and the CVaR inequality representing the feasibility conditions as constraint conditions. Next, the sample average approximation problem of the CVaR-SP model is presented by using the Monte Carlo method and the smoothing method. Subsequently, the conditions for the convergence of the sample average approximation problem are analyzed. Finally, the penalized sample average approximation algorithm is used to solve the problem, the related numerical results further verify the validity of the method.