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On the convergence of s-dependent GFR conjugate gradient method for unconstrained optimization

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Abstract

In this paper, the authors present an s-dependent conjugate gradient method for unconstrained optimization problem and make two different kinds of estimations of upper bounds of β k with respect to \(\beta_{k}^{\mathrm{FR}}\) which are called dependent ratio. The global convergence of s-dependent GFR conjugate gradient method using several step-size rules is obtained.

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Authors and Affiliations

  1. School of Science, Shandong University of Technology, Zibo, 255049, People’s Republic of China

    Wenling Zhao & Yajing Gu

  2. Institute of Operations Research, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Changyu Wang

Authors
  1. Wenling Zhao
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  2. Changyu Wang
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  3. Yajing Gu
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Corresponding author

Correspondence to Wenling Zhao.

Additional information

This research was supported by the National Natural Science Foundations of China (11271233) and Natural Science Foundation of Shandong Province (ZR2012AM016).

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Zhao, W., Wang, C. & Gu, Y. On the convergence of s-dependent GFR conjugate gradient method for unconstrained optimization. Numer Algor 78, 721–738 (2018). https://doi.org/10.1007/s11075-017-0397-7

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  • DOI: https://doi.org/10.1007/s11075-017-0397-7

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