A New Nonmonotone Trust Region Barzilai-Borwein Method for Unconstrained Optimization Problems

In this paper, we propose a new nonmonotone trust region Barzilai-Borwein (BB for short) method for solving unconstrained optimization problems. The proposed method is given by a novel combination of a modified Metropolis criterion, BB-stepsize and trust region method. The new method uses the reciprocal of BB-stepsize to approximate the Hessian matrix of the objective function in the trust region subproblems, and accepts some bad solutions according to the modified Metropolis criterion based on simulated annealing idea. Under some suitable assumptions, the global convergence of the new method is established. Some preliminary numerical results indicate that, the new method is more efficient compared with the existing trust region BB method.