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A modified nonlinear Polak–Ribière–Polyak conjugate gradient method with sufficient descent property

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Abstract

In this paper, a small and necessary revision on an assumption condition of Aminifard and Babaie-Kafaki (Calcolo, 2019. https://doi.org/10.1007/s10092-019-0312-9) is made. By a little modification, a new conjugate gradient method is proposed, in which the search directions satisfy the sufficient descent condition with the strong Wolfe line search. The main difference between two algorithms is that the proposed method is globally convergent without boundedness assumption on the steplength. Comparative numerical results demonstrating efficiency of the proposed method are reported.

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Notes

  1. If Powell’s restart criterion \(g_{k}^Tg_{k-1}\ge 0.2 ||g_k||^2\) is satisfied, then the search direction is calculated as \(d_k=-g_k\).

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Acknowledgements

This work is supported by National Natural Science Foundation of China (11601012), National Science Fund for Distinguished Young Scholars (11625105). We would like to thank Professors N. Andrei for his THREECG code for numerical comparison.

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Authors and Affiliations

  1. College of Science, Xi’an Shiyou University, Xi’an, 710065, People’s Republic of China

    Xiaoliang Dong

  2. School of Mathematics Science, Nanjing Normal University, Nanjing, People’s Republic of China

    Xiaoliang Dong

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  1. Xiaoliang Dong
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Correspondence to Xiaoliang Dong.

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The work of the first author was done while he was visiting Xi’an Shiyou University.

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Dong, X. A modified nonlinear Polak–Ribière–Polyak conjugate gradient method with sufficient descent property. Calcolo 57, 30 (2020). https://doi.org/10.1007/s10092-020-00378-2

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  • DOI: https://doi.org/10.1007/s10092-020-00378-2

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