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A Class of Accelerated Subspace Minimization Conjugate Gradient Methods

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  • Wumei Sun

    (Xidian University)

  • Hongwei Liu

    (Xidian University)

  • Zexian Liu

    (Guizhou University)

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.

Suggested Citation

  • Wumei Sun & Hongwei Liu & Zexian Liu, 2021. "A Class of Accelerated Subspace Minimization Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 811-840, September.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01897-w
    DOI: 10.1007/s10957-021-01897-w
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    References listed on IDEAS

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    1. Neculai Andrei, 2020. "Nonlinear Conjugate Gradient Methods for Unconstrained Optimization," Springer Optimization and Its Applications, Springer, number 978-3-030-42950-8, December.
    2. Neculai Andrei, 2020. "Diagonal Approximation of the Hessian by Finite Differences for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 859-879, June.
    3. Neculai Andrei, 2020. "General Convergence Results for Nonlinear Conjugate Gradient Methods," Springer Optimization and Its Applications, in: Nonlinear Conjugate Gradient Methods for Unconstrained Optimization, chapter 0, pages 89-123, Springer.
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    Cited by:

    1. Deng, Huaijun & Liu, Linna & Fang, Jianyin & Qu, Boyang & Huang, Quanzhen, 2023. "A novel improved whale optimization algorithm for optimization problems with multi-strategy and hybrid algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 794-817.

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