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A new modified nonmonotone adaptive trust region method for unconstrained optimization

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Abstract

In this paper, we present an adaptive trust region method for solving unconstrained optimization problems which combines nonmonotone technique with a new update rule for the trust region radius. At each iteration, our method can adjust the trust region radius of related subproblem. We construct a new ratio to adjust the next trust region radius which is different from the ratio in the traditional trust region methods. The global and superlinear convergence results of the method are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems.

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Acknowledgements

The authors would like to thank the editor and the reviewers for their insightful and constructive comments, which help to enrich the content and improve the presentation of this paper.

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  1. Department of Mathematics and Physics, Shandong Jiaotong University, Jiaoxiao Road, Jinan, Shandong Province, 250023, China

    Zhaocheng Cui

  2. Department of Mathematics, Harbin Institute of Technology, Harbin, 150080, P. R. China

    Boying Wu

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  1. Zhaocheng Cui
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  2. Boying Wu
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Correspondence to Zhaocheng Cui.

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Cui, Z., Wu, B. A new modified nonmonotone adaptive trust region method for unconstrained optimization. Comput Optim Appl 53, 795–806 (2012). https://doi.org/10.1007/s10589-012-9460-4

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  • DOI: https://doi.org/10.1007/s10589-012-9460-4

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