Studies On A Class Of Penalty Method For Solving Linear Complementarity Problems

Complementarity problems(CPs) not only become the basic problem in mathematical programming via the close relations to linear programming, quadratic programming and the optimality conditions of constrained optimization problems, but the complementarity problems themselves are an important branch of operations research. Theories and algorithms of CPs have been widely used in the field of mechanics, transportation, economy, finance, control etc.. Therefore, the research on algorithm for solving CPs is always the hot spots in applied mathematics and computational mathematics.This thesis firstly genaralizes a class of penalty function method for linear complementarity problems(LCPs) by using penalty function technology. Then constructs a new penalty function method for solving LCPs based on the method above and discusses the convergence property of the new method.This thesis is divided into three chapters, the results of each part are as follows:The first chapter is the introduction, which introduces the basic knowledge related to LCPs, then describes the histotical background and present research conditions of the penalty function method for solving LCPs.The second chapter uses the penalty function method for solving LCPs proposed by S. Wang and X. Q. Yang(2008). Under some assumptions, this chapter proves the convergence results when the matrix of LCPs is a P-matrix which is much more relaxed than the positive definite assumption in S. Wang and X. Q. Yang.In the third chapter, we construct a new penalty function method for solving LCPs based on the penalty function method discussed in chapter two and study the convergence property of the new method under some assumptions. The result shows that the error bound in the new method is smaller than that of chapter two when k∈(0,1).