On determining radius in nonmonotone trust-region approaches

Document Type : Research Article


1 Department of Mathematics, Faculty of Science, Razi University,Kermanshah, Iran

2 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.


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