Study The Inexact Method For Nonlinear Complementarity Problem

Complememtarity problem was first proposed in 1963.Since then it has been the hotspot in the research of mathematical programming field. Also many algorithms have been proposed. The thesis mainly deals with the studies of inexact algorithms for nonlinear complementarity problems. We propose an inexact solution, in order to solve the difficult of the exact solution for its subproblem. On the one hand, the thesis bases on the idea of Qi's smoothing Newton method and the theory of seimsmooth, with the smooth type of the Fisher-Burmeister function, NCP is converted into a smoothing nonlinear equations and smoothing inexact Newton method is used to solve the equations, Numerical results indicate that the algorithm is effective. The other hand, the trust region method has strong convergence and reliability, with the smooth approach function of the Fisher-Burmeister function, NCP is converted into an unconstrained optimization problem, we propose a nonmonotonic inexact trust region algorithm for unconstrained optimization. We employ both the nonmonotonic Wolfe line search technique and trust region method, the inexact solution of subproblem generate trail step. At every iteration, nonmonotonic Wolfe line search is used to solve the next iteration when it is not accepted. Under generalized conditions, the level set includes a sequence by algorithm, and at least, NCP's solution is it's an accumulation point, the global and superlinear convergance of the algorithm are proved.