| Complementarity problems have wide applications in many fields of scientific research and engineering technology.Studying the theory and algorithm of the complementarity problems is a hot issue in the field of computational mathematics and operations research.In this thesis,we mainly propose three new algorithms for solving the nonlinear complementarity problems,which are based on results of previous studies,and we study the convergence of these algorithms.The thesis is divided into five chapters:In the first chapter,we describe the research on the nonlinear complementarity problems in domestic and foreign.In the second chapter,we propose a modulus-based matrix splitting method with inner iteration for a class of nonlinear complementarity problems.Convergence conditions of the iteration method are analyzed carefully,which shows that the iteration sequence generated by this method converges to a solution of the NCP under certain conditions.Moreover,the convergence conditions of the proposed method are studied when the system matrix is symmetric positive definite or is an H+-matrix.Theoretical results are supported by the numerical experiments,which implies the proposed method is effective.In the third chapter,we propose a general modulus-based matrix splitting it-eration method for a class of weakly nonlinear complementarity problems.And we analyze the convergence of the proposed method in certain conditions.Finally,we show the effectiveness of our algorithm through the experiments.In the forth chapter,we propose a general accelerated modulus-based matrix splitting iteration method for solving a class of weakly nonlinear complementarity problems.And we analyze the convergence conditions of the method.Numerical ex-periments show that the proposed method is efficient in accelerating the convergence performance.In the last chapter,we give a summary of our research in this thesis,and give some questions for further research. |
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