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An improved nonmonotone adaptive trust region method

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Abstract

Trust region methods are a class of effective iterative schemes in numerical optimization. In this paper, a new improved nonmonotone adaptive trust region method for solving unconstrained optimization problems is proposed. We construct an approximate model where the approximation to Hessian matrix is updated by the scaled memoryless BFGS update formula, and incorporate a nonmonotone technique with the new proposed adaptive trust region radius. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some suitable and standard assumptions, it is shown that the proposed algorithm possesses global convergence and superlinear convergence. Numerical results demonstrate that the proposed method is very promising.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi, 710126, People’s Republic of China

    Yanqin Xue & Hongwei Liu

  2. School of Mathematics and Computer Science, Hezhou University, Hezhou, 542899, People’s Republic of China

    Zexian Liu

Authors
  1. Yanqin Xue
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  2. Hongwei Liu
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  3. Zexian Liu
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Corresponding authors

Correspondence to Yanqin Xue, Hongwei Liu or Zexian Liu.

Additional information

This research is supported by National Science Foundation of China (No. 11461021), Shaanxi Science Foundation (No. 2017JM1014), and Guangxi Science Foundation (Nos. 2018GXNSFBA281180).

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Xue, Y., Liu, H. & Liu, Z. An improved nonmonotone adaptive trust region method. Appl Math 64, 335–350 (2019). https://doi.org/10.21136/AM.2019.0138-18

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  • DOI: https://doi.org/10.21136/AM.2019.0138-18

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