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An efficient nonmonotone trust-region method for unconstrained optimization

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Abstract

The monotone trust-region methods are well-known techniques for solving unconstrained optimization problems. While it is known that the nonmonotone strategies not only can improve the likelihood of finding the global optimum but also can improve the numerical performance of approaches, the traditional nonmonotone strategy contains some disadvantages. In order to overcome to these drawbacks, we introduce a variant nonmonotone strategy and incorporate it into trust-region framework to construct more reliable approach. The new nonmonotone strategy is a convex combination of the maximum of function value of some prior successful iterates and the current function value. It is proved that the proposed algorithm possesses global convergence to first-order and second-order stationary points under some classical assumptions. Preliminary numerical experiments indicate that the new approach is considerably promising for solving unconstrained optimization problems.

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Authors and Affiliations

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

    Masoud Ahookhosh & Keyvan Amini

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  1. Masoud Ahookhosh
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  2. Keyvan Amini
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Correspondence to Keyvan Amini.

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Ahookhosh, M., Amini, K. An efficient nonmonotone trust-region method for unconstrained optimization. Numer Algor 59, 523–540 (2012). https://doi.org/10.1007/s11075-011-9502-5

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