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Two classes of spectral conjugate gradient methods for unconstrained optimizations

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Abstract

The spectral conjugate gradient method is effective iteration method for solving large-scale unconstrained optimizations. In this paper, using the strong Wolfe line search to yield the spectral parameter, and giving two approaches to choose the conjugate parameter, then two classes of spectral conjugate gradient methods are established. Under usual assumptions, the proposed methods are proved to possess sufficient descent property and global convergence. Taking some specific existing conjugate parameters to test the validity of the two classes of methods, and choosing the best method from each class to compare with other efficient conjugate gradient methods, respectively. Large-scale numerical results for the experiments are reported, which show that the proposed methods are promising.

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Authors and Affiliations

  1. College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, China

    Jinbao Jian & Xianzhen Jiang

  2. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China

    Pengjie Liu

  3. School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Chen Zhang

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  1. Jinbao Jian
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  2. Pengjie Liu
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  3. Xianzhen Jiang
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  4. Chen Zhang
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Correspondence to Xianzhen Jiang.

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This work is supported in part by the National Natural Science Foundation of China (No. 12171106), and in part by the Natural Science Foundation of Guangxi Province (Nos. 2020GXNSFDA238017, 2018GXNSFFA281007), and in part by Research Project of Guangxi University for Nationalities (No. 2018KJQD02).

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Jian, J., Liu, P., Jiang, X. et al. Two classes of spectral conjugate gradient methods for unconstrained optimizations. J. Appl. Math. Comput. 68, 4435–4456 (2022). https://doi.org/10.1007/s12190-022-01713-2

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  • DOI: https://doi.org/10.1007/s12190-022-01713-2

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