| In this thesis, we mainly discuss the numerical algorithms for solving comple-mentarity problems. There are lots of problems from engineering, economics, and finance which can be modeled as complementarity problems, such as the static traf-fic equilibrium problem, price equilibrium, supply chain problem. There are three chapters in this thesis.In the Introduction, the current situation and background about complementar-ity problems as well as some conceptions which will appear in the following chapters are introduced.In Chapter one, a modified semismoothing asymptotically Newton method for solving the nonlinear complementarity problems (NCP)is proposed. In order to solve the NCP, the NCP are reformulated as a semismoothing system of equations with a simple bounded constrain. Then a modified asymptotically Newton method is proposed for solving the semismoothing system of equations. The algorithm only perform one Amijo line search and only solve one linear equations per iteration. The global and superlinear convergence of the method are proved under some suitable assumptions. Some numerical results are included to highlight the effectiveness of the modified algorithm.In Chapter two, the numerical algorithms for solving a class of stochastic linear complementarity problems(SLCP) are discussed. The use of the modified algorithm which mentioned in the former chapter is extended. First, the SLCP are refor-mulated as a semismoothing system of equations by the Fischer-Burmeister NCP function and a slack variable. Then the modified semismoothing asymptotically Newton method for solving the SLCP is proved to be feasible. The global and su-perlinear convergence of the method are proved under some suitable assumptions. Further more, the numerical results are included to illustrate the effectiveness and feasibility of the modified algorithm.In the last chapter, we make a conclusion of our work. Some problems needed to be solved are pointed out... |
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