The Fast Iterative Algorithms For Some Stochastic Nonlinear Complementarity Problems

Many practical application models can be described by nonlinear complementarity problems.For nonlinear complementarity problems,we study the mixed complementarity problem,the stochastic mixed complementarity problem and the stochastic implicit complementarity problem.Modulus-based matrix splitting iterative method is an effective method to solve nonlinear complementary problems.In this paper,a fast algorithm for stochastic nonlinear complementarity problem is constructed by combining the Modulus-based matrix iterative method,The details are as follows:Firstly,we propose smoothing modulus-based iteration method to solve the mixed complementary problem.The mixed complementary problem is transformed into an equivalent modular equation,and then the equation system with absolute value is used to approximate the original problem with a smoothing function,the convergence analysis is obtained,and the toll design experiment shows that the method is effective.Secondly,based on the deterministic mixed complementarity problem,the expected value model is used to transform the stochastic mixed complementarity problem into a mixed complementarity problem,and then using the variable transformation,we transform the nonlinear complementarity problem into a fixed-point equations;Then,a smooth modulus-based iterative method is constructed to solve the fixed-point equations,and the convergence analysis of the algorithm and the numerical experimental results of stochastic traffic equilibrium are given.Thirdly,we extend the idea of modular iteration method,modified Newton method and m +1-step iteration method to solve the implicit complementarity problems,and propose a smooth modulus-based iterative method for solving it,the numerical examples demonstrate the effectiveness of the method.Then,we propose a smooth modulus-based iterative method to solve stochastic implicit complementarity problems.