A nonmonotone trust region method for unconstrained optimization

In this paper, we propose a nonmonotone trust region method for unconstrained optimization. Our method can be regarded as a combination of nonmonotone technique, fixed steplength and trust region method. When a trial step is not accepted, the method does not resolve the subproblem but generates a iterative point whose steplength is defined by a formula. We only allow increase in function value when trial steps are not accepted in close succession of iterations. Under mild conditions, we prove that the algorithm is global convergence and superlinear convergence. Primary numerical results are reported.