Modulus-based Iterative Methods For Solving A Class Of Weakly Nonlinear Complementarity Problems

The complementary problem has been widely applied in many fields of scientific research and engineering technology.Studying the theory and algorithm of the comple-mentarity problems is a hot issue in the field of computational mathematics and operations research.In this paper,we analyed the property and algorithm of the nonlinear comple-mentarity problem,which are based on results of previous studies.The main content of this paper is organized as follows:In Chapter 1,the development and research status of the nonlinear complementarity problems are summarized,and some basic definitions and notations are introduced.In Chapter 2,we proved that the coefficient matrix is-matrix of complementary problem can be converted into an equivalent complementary problem,whose coefficien-t matrix is strictly diagonally dominant.In addition,new convergence theories of the modulus-based matrix splitting iteration method are given for the nonlinear complemen-tarity problem with the weaker condition.In Chapter 3,we studied the modulus-based matrix splitting iteration method for solving the nonlinear complementarity problem,given a weaker convergence theorem for the modulus-based matrix splitting iteration method.Furthermore,we improved the convergence theorem for the accelerated modulus-based matrix splitting iteration method.In Chapter 4,the relaxation two-sweep modulus-based matrix splitting iteration method is proposed to solve the nonlinear complementarity problem,and the effect of the positive diagonal matrixΩon the relaxation two-sweep modulus-based AOR method are analyzed when the coefficient matrixis_+-matrix.Experiments show that the algorithm is very effective.In addition,the experimental results show that the relaxation two-sweep modulus-based matrix splitting iteration method can be guaranteed to have better experimental results than the modulus-based matrix splitting iteration method by proper selection of parameters.In Chapter 5,on the basis of the subspace method,we establish the modulus-based preconditioned Krylov subspace method for solving nonlinear complementarity problem.Experiments show that the proposed algorithm is very effective for solving nonlinear com-plementarity problems.In Chapter 6,the research work of this thesis is summarized,and put forward the idea of future research work and the problem to be solved.