Some Studies On Numerical Methods For The Complementarity Problems

The methods of nonlinear complementarity problems and extended linear com-plementarity problems are studied in this thesis. The two types complementar-ity problems are widely used in engineering, economics, transportation and so on. They've become hot spots in computational and nonlinear science.In the Introduction, background and kinds of the complementarity problem are outlined. At the same time, the main idea, origin and development of trust region filter are introduced.In Chapter one, the nonlinear complementarity problem is equivalent to a min-imization problems with non-negative constraints, which is solved by filter, instead of the penalty function, with the trust region SQP method. Algorithm suitable qualitative and global convergence are proved under some suitable assumptions. Several numerical experiments are used to show the feasibility and effectiveness of the algorithm.In Chapter two, the extended linear complementary problem is studied. The one-step smoothing Newton method is designed to solve it. The convergence of the algorithm is proved under some suitable assumptions. Several numerical experiments are used to show the feasibility and effectiveness of the algorithm.In Chapter three, we make a summary of the work, as well as introduce the research progress and achievement of the subject. In the end, some suggestions for further study are pointed out.