A New Filter Nonmonotone Adaptive Trust Region Method for Unconstrained Optimization

In this paper, a new filter nonmonotone adaptive trust region with fixed step length for unconstrained optimization is proposed. The trust region radius adopts a new adaptive strategy to overcome additional computational costs at each iteration. A new nonmonotone trust region ratio is introduced. When a trial step is not successful, a multidimensional filter is employed to increase the possibility of the trial step being accepted. If the trial step is still not accepted by the filter set, it is possible to find a new iteration point along the trial step and the step length is computed by a fixed formula. The positive definite symmetric matrix of the approximate Hessian matrix is updated using the MBFGS method. The global convergence and superlinear convergence of the proposed algorithm is proven by some classical assumptions. The efficiency of the algorithm is tested by numerical results.