| The complementarity problem is one of the most important topics in optimization, having close relationship with the mathematical programming, the variational inequality, the fixed point problem, and the generalized equation and so on. It is an interdisciplinary field which comes from applied mathematics, computational mathematics and fundamental mathematics. The complementarity problem has a wide application in many fields such as engineering design, optimal control, information technology and economic equilibrium. Since some elements may involve uncertain data in many practical problems, the stochastic versions of complementarity problems have drawn much attention in the recent literature. Generally speaking, we cannot expect that there exists a vector satisfying all the constraints in these stochastic complementarity problems. Therefore, how to find an appropriate and reasonable solution in stochastic complementarity problems is always a hot issue for mathematicians and experts in other related fields.In this paper, we focus on the study of methods for a class of stochastic complementarity problems. Firstly, we present a brief review of the origin and historical development of the complementarity problems and give introduction of some optimization models for solving stochastic complementarity problems. Secondly, we study a function to formulate the considered problem as a system of semismooth equations and further a constrained minimization problem. This function is a combination of an NCP-function and maximum function. A semismooth Newton method is also given. Moreover, by employing a smoothing NCP function, the considered problem is equivalent to a smoothing constrained minimization problem, which can be solved by a smoothing Newton method with some perturbing technique. The convergences of two methods have been proved in theory. Number results show that our methods are promising. Finally, the summarization and future prospects of this thesis are given.
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