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A Class of Accelerated Subspace Minimization Conjugate Gradient Methods

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Abstract

The subspace minimization conjugate gradient methods based on Barzilai–Borwein method (SMCG_BB) and regularization model (SMCG_PR), which were proposed by Liu and Liu (J Optim Theory Appl 180(3):879–906, 2019) and Zhao et al. (Numer Algorithm, 2020. https://doi.org/10.1007/s11075-020-01017-1), respectively, are very interesting and efficient for unconstrained optimization. In this paper, two accelerated subspace minimization conjugate gradient methods are proposed for unconstrained optimization. Motivated by the subspace minimization conjugate gradient methods and the finite termination of linear conjugate gradient methods, we derive an acceleration parameter by the quadratic interpolation function to improve the stepsize, and the modified stepsize may be more closer to the stepsize obtained by exact line search. Moreover, several specific acceleration criteria to enhance the efficiency of the algorithm are designed. Under standard conditions, the global convergence of the proposed methods can be guaranteed. Numerical results show that the proposed accelerated methods are superior to two excellent subspace minimization conjugate gradient methods SMCG_BB and SMCG_PR.

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for their valuable suggestions and comments which have greatly improved the presentation of this paper. This research is supported by the National Natural Science Foundation of China (No. 11901561) and Guangxi Natural Science Foundation (No. 2018GXNSFBA281180).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710126, China

    Wumei Sun & Hongwei Liu

  2. School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China

    Zexian Liu

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  1. Wumei Sun
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  2. Hongwei Liu
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  3. Zexian Liu
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Correspondence to Hongwei Liu.

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Communicated by Nobuo Yamashita.

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Sun, W., Liu, H. & Liu, Z. A Class of Accelerated Subspace Minimization Conjugate Gradient Methods. J Optim Theory Appl 190, 811–840 (2021). https://doi.org/10.1007/s10957-021-01897-w

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