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An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

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Abstract

Trust region method is a robust method for optimization problems. In this paper, we propose a novel adaptive nonmonotone technique based on trust region methods for solving unconstrained optimization. In order to accelerate the convergence of trust region methods, an adaptive trust region is generated according to the Hessian of the iterate point. Both the nonmonotone techniques and this adaptive strategies can improve the trust region methods in the sense of convergence. We prove that the proposed method is locally superlinear convergence under some standard assumptions. Numerical results show that the new method is effective and has a high speed of convergence in practice.

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Acknowledgements

The authors gratefully appreciate the valuable suggestions from the anonymous referees for careful reading and many useful suggestions, which improve the paper. We also thank the financial support from China National Petroleum Corporation (Grant No. 2014B-1709).

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Authors and Affiliations

  1. School of Science, China University of Petroleum, Beijing, 102249, China

    Jianjun Liu, Xiangmin Xu & Xuehui Cui

Authors
  1. Jianjun Liu
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  2. Xiangmin Xu
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  3. Xuehui Cui
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Corresponding author

Correspondence to Xuehui Cui.

Appendix

Appendix

Table 4 Test problems set
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Liu, J., Xu, X. & Cui, X. An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization. Comput Optim Appl 69, 77–97 (2018). https://doi.org/10.1007/s10589-017-9941-6

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  • DOI: https://doi.org/10.1007/s10589-017-9941-6

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