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Hybrid Riemannian conjugate gradient methods with global convergence properties

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  • Hiroyuki Sakai

    (Meiji University)

  • Hideaki Iiduka

    (Meiji University)

Abstract

This paper presents Riemannian conjugate gradient methods and global convergence analyses under the strong Wolfe conditions. The main idea of the proposed methods is to combine the good global convergence properties of the Dai–Yuan method with the efficient numerical performance of the Hestenes–Stiefel method. One of the proposed algorithms is a generalization to Riemannian manifolds of the hybrid conjugate gradient method of the Dai and Yuan in Euclidean space. The proposed methods are compared well numerically with the existing methods for solving several Riemannian optimization problems. Python implementations of the methods used in the numerical experiments are available at https://github.com/iiduka-researches/202008-hybrid-rcg .

Suggested Citation

  • Hiroyuki Sakai & Hideaki Iiduka, 2020. "Hybrid Riemannian conjugate gradient methods with global convergence properties," Computational Optimization and Applications, Springer, vol. 77(3), pages 811-830, December.
    • Handle: RePEc:spr:coopap:v:77:y:2020:i:3:d:10.1007_s10589-020-00224-9
    DOI: 10.1007/s10589-020-00224-9
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    References listed on IDEAS

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    1. 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.
    2. Hiroyuki Sato, 2016. "A Dai–Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions," Computational Optimization and Applications, Springer, vol. 64(1), pages 101-118, May.
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    Cited by:

    1. Sakai, Hiroyuki & Sato, Hiroyuki & Iiduka, Hideaki, 2023. "Global convergence of Hager–Zhang type Riemannian conjugate gradient method," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    2. Yasushi Narushima & Shummin Nakayama & Masashi Takemura & Hiroshi Yabe, 2023. "Memoryless Quasi-Newton Methods Based on the Spectral-Scaling Broyden Family for Riemannian Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 639-664, May.
    3. Hiroyuki Sakai & Hideaki Iiduka, 2024. "Modified Memoryless Spectral-Scaling Broyden Family on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 834-853, August.
    4. Hiroyuki Sakai & Hideaki Iiduka, 2021. "Sufficient Descent Riemannian Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 130-150, July.

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