The Research Of Penalty Method For Solving Mixed Linear Complementarity Problems

Numerical methods for mixed linear complementarity problems are an important topic of computational mathematics and penalty methods are a class of important approximate methods for solving complementarity problems. Recently, scholars at home and abroad have paid lots of attention to construct penalty methods for solving complementarity problems. But there are very few works for the mixed linear complementarity problem. In this paper, we study the penalty methods to solve mixed linear complementarity problems. Under proper conditions, the convergence of the method is verified. Additionally, we propose two simple iterative algorithms to solve the penalized equation and study their convergence. N umerical results show the effectiveness of the iterative algorithms.This paper is divided into three chapters. In C hapter 1, we shall give the background of the problem, the progress in research of penalty methods for solving complementarity problems and we will introduce some important concepts and some related properties and the contents of this paper. In Chapter 2, the penalty method is proposed to solve the mixed linear complementarity problem, and the existence and the uniqueness of the solution of penalized equation are given. Also, the convergence properties is analyzed. In the last chapter, two simple iterative algorithms are proposed to solve the penalized equations. Under proper conditions, we prove that the iterative sequences monotonically converge to the solution of the penalized equations. Numerical experiments show the effectiveness of the iterative algorithms.