Modulus-based Matrix Splitting Iteration Methods For Stochastic Complementarity Problems

In the real-world applications,many problems,such as engineering,finance,and transportation and so on,can be modeled as the stochastic linear complementarity problems.In this paper,some numerical algorithms are studied for solving the stochastic linear complementary problems.The basic idea is that the problems are first transformed into the linear complementarity problems through the expected value formulation.Then we transform the linear complementarity problem into an equivalent fixed point equations by using variable transformation.Finally a series of the modulus-based matrix splitting iteration methods are constructed to solve the fixed point equations.The details are as follows:Firstly,some modulus-based matrix iteration methods and the regularized modulus-based matrix iteration methods for solving stochastic linear complementarity problems are constructed,and the convergence theory of the algorithms are given.The feasibility of the methods is verified by numerical experiments.Secondly,some modulus-based matrix splitting iteration methods and the regularized modulus-based matrix splitting iteration methods for solving stochastic linear complementary problems are constructed,and the convergence of the methods are proved.The effectiveness of the methods is verified by numerical experiments.Thirdly,some modulus-based matrix multi-splitting iteration methods and regularized modulus-based matrix multi-splitting iteration methods are presented to solve the large-scale problems,which can make the problem divided into several small scales problems.The convergence and numerical results of the methods are given.At last,based on the modulus-based matrix multi-splitting iteration methods,the modulus-based matrix two-stage multi-splitting iteration methods and the regularized modulus-based matrix two-stage multi-splitting iteration methods are constructed to solve the stochastic linear complementarity problems.The convergence of the algorithms are discussed,and the effectiveness of the method is verified by numerical experiments.