A NEW SMOOTHING NONMONOTONE TRUST REGION METHOD FOR SOLVING NONLINEAR COMPLEMENTARITY PROBLEMS

In this paper, we propose a new smoothing nonmonotone trust region method for solving nonlinear complementarity problems with P-0 -functions. First, the nonlinear complementarity 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 an iterative point whose steplength 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 complementarity condition.