A New Smoothing Nonmonotone Trust Region Method for Solving Nonlinear Complementarity Problems

摘要

In this paper, we propose one new smoothing nonmonotone trust region method for solving nonlinear complementarily problems with P_0 - functions. First, the nonlinear complementarily problem (NCP) is reformulated as a nonsmooth equation. Then on the basis of the reformulation, a smoothing nonmonotone trust region algorithm via a line search for solving the NCP with P_0 - functions is proposed. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates a iterative point whose step length is generated by a formula. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under a nonsingularity condition, the superlinear convergence of the algorithm is established without the strict complementarily condition.