Document Type : Research Article
Department of Mathematics, Faculty of Science, Razi University,Kermanshah, Iran
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
This paper proposes two effective nonmonotone trust-region frameworks for solving nonlinear unconstrained optimization problems while provide a new effective policy to update the trust-region radius. Conventional nonmonotone trust-region algorithms apply a specific nonmonotone ratio to accept new trial step and update the trust-region radius. This paper recommends using the nonmonotone ratio only as an acceptance criterion for a new trial step. In contrast, the monotone ratio or a hybrid of monotone and nonmonotone ratios is proposed as a criterion for updating the trust-region radius. We investigate the global convergence to first- and second-order stationary points for the proposed approaches under certain classical assumptions. Initial numerical results indicate that the proposed methods significantly enhance the performance of nonmonotone trust-region methods.