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A Spectral Conjugate Gradient Method with Descent Property

Author

Listed:
  • Jinbao Jian

    (College of Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, China)

  • Lin Yang

    (College of Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, China)

  • Xianzhen Jiang

    (College of Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, China)

  • Pengjie Liu

    (College of Mathematics and Information Science, Guangxi University, Nanning 530004, Guangxi, China)

  • Meixing Liu

    (Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, China)

Abstract

Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a core work. And the aim of this paper is to propose a new and effective alternative method for these two parameters. First, motivated by the strong Wolfe line search requirement, we design a new spectral parameter. Second, we propose a hybrid conjugate parameter. Such a way for yielding the two parameters can ensure that the search directions always possess descent property without depending on any line search rule. As a result, a new SCGM with the standard Wolfe line search is proposed. Under usual assumptions, the global convergence of the proposed SCGM is proved. Finally, by testing 108 test instances from 2 to 1,000,000 dimensions in the CUTE library and other classic test collections, a large number of numerical experiments, comparing with both SCGMs and CGMs, for the presented SCGM are executed. The detail results and their corresponding performance profiles are reported, which show that the proposed SCGM is effective and promising.

Suggested Citation

  • Jinbao Jian & Lin Yang & Xianzhen Jiang & Pengjie Liu & Meixing Liu, 2020. "A Spectral Conjugate Gradient Method with Descent Property," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:280-:d:322557
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    References listed on IDEAS

    as
    1. C. X. Kou & Y. H. Dai, 2015. "A Modified Self-Scaling Memoryless Broyden–Fletcher–Goldfarb–Shanno Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 209-224, April.
    2. Y.H. Dai & Y. Yuan, 2001. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 33-47, March.
    3. Avinoam Perry, 1978. "Technical Note—A Modified Conjugate Gradient Algorithm," Operations Research, INFORMS, vol. 26(6), pages 1073-1078, December.
    4. N. Andrei, 2009. "Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 249-264, May.
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