A Class Of Smoothing SAA Methods For A Stochastic Nonlinear Complementarity Problem

Stochastic variational inequalities and stochastic complementarity problems, as impor-tant topics of mathematical programming, have many applications in many fields such as en-gineering design, optimal control, information technology and economic equilibrium.Sample average approximation method is one of the effective approaches for solving stochastic comp-lementarity problem. The basic idea of sample average approximation method is to generate an independent identically distributed sample of randam variable, and then approximate the expected value with sample average. Further, the sample average problem is solved by deterministic optimization methods. The solution of the sample average problem is a reasonable approximation solution of the true problem.In this paper, we discuss a smoothing sample average approximation method for a stochastic nonlinear complementarity problem on the basis of previous work. First,we consider an EV model for SNCP and use the Fischer-Burmeister function to reformulate the EV model as an unconstrained minimization problem.Then we employ the sample average approximation method and smoothing techniques to give approximation problems for the unconstrained minmization problem. Convergence analysis is given. We finally apply these results to supply chain network equilibrium problem with random demands and give some preliminary numerical results.