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A model-hybrid approach for unconstrained optimization problems

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Abstract

In this paper, we propose a model-hybrid approach for nonlinear optimization that employs both trust region method and quasi-Newton method, which can avoid possibly resolve the trust region subproblem if the trial step is not acceptable. In particular, unlike the traditional trust region methods, the new approach does not use a single approximate model from beginning to the end, but instead employs quadratic model or conic model at every iteration adaptively. We show that the new algorithm preserves the strong convergence properties of trust region methods. Numerical results are also presented.

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Authors and Affiliations

  1. Department of Mathematics, Taiyuan Normal University, Taiyuan, 030012, China

    Fu-Sheng Wang & Chuan-Long Wang

  2. College of Mathematics and Information Science, Yulin Normal University, Yulin, Guangxi, 537000, China

    Jin-Bao Jian

Authors
  1. Fu-Sheng Wang
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  2. Jin-Bao Jian
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  3. Chuan-Long Wang
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Corresponding author

Correspondence to Fu-Sheng Wang.

Additional information

This work is supported by the National Natural Science Foundation of China (11171250); The Natural Science Foundation of Shanxi Province of China (2011011002-2)

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Wang, FS., Jian, JB. & Wang, CL. A model-hybrid approach for unconstrained optimization problems. Numer Algor 66, 741–759 (2014). https://doi.org/10.1007/s11075-013-9757-0

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