A New Nonmonotone Trust Region Algorithm Based on Simulated Annealing and Barzilai–Borwein Methods for Unconstrained Optimization

In this paper, a new nonmonotone trust region algorithm based on a novel combination of a nonmonotone strategy, a modified Metropolis criterion, and the Barzilai–Borwein step size is proposed. The proposed algorithm uses the reciprocal of Barzilai–Borwein step size 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 the simulated annealing idea. Under some mild assumptions, the global convergence of the algorithm is established. Some preliminary numerical results indicate that the new algorithm performs well with high efficiency.