Modulus-based Matrix Splitting Iteration Method For Implicit Complementarity Problem

Complementarity problem is widely used in the economy and engineering area.This paper mainly discusses some fast iterative methods for solving a general implicit complementarity problem. Firstly, by using the technique of appropriate change of variables, implicit complementarity problem can be transformed into fixed point problem,so we establish modulus-based matrix splitting iteration method, modulus-based synchronous multi-splitting iteration method and modulus-based two-stage splitting iteration method, and discuss the convergence theory of them under some restrictive conditions. Numerical experiments confirm the theoretical analysis, and show that the proposed methods are efficientThis paper includes five chapters:The background knowledge and current situation of complementarity problems, and some necessary notations and lemmas are given in Chapter 1.In Chapter 2, the modulus-based matrix splitting iteration methods for implicit complementarity problem and their convergence analysis are introduced. In addition,some optimization methods for implicit complementarity problem are presented. At last,the numerical experiments are given.In Chapter 3, the modulus-based synchronous multi-splitting iteration methods and modulus-based triangular multi-splitting iteration method are presented, and analysis their convergence. At last, some numerical experiments are presented.Modulus-based two-stage splitting iteration methods, modulus-based two-stage triangular splitting iteration methods and their convergence analysis are introduced in Chapter 4.The paper was summarized in Chapter 5.