IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v441y2023ics0096300322007536.html
   My bibliography  Save this article

Global convergence of Hager–Zhang type Riemannian conjugate gradient method

Author

Listed:
  • Sakai, Hiroyuki
  • Sato, Hiroyuki
  • Iiduka, Hideaki

Abstract

This paper presents the Hager–Zhang (HZ)-type Riemannian conjugate gradient method that uses the exponential retraction. We also present global convergence analyses of our proposed method under two kinds of assumptions. Moreover, we numerically compare our proposed methods with the existing methods by solving two kinds of Riemannian optimization problems on the unit sphere. The numerical results show that our proposed method has much better performance than the existing methods, i.e., the FR, DY, PRP, and HS methods. In particular, they show that it has much higher performance than existing methods including the hybrid ones in computing the stability number of graphs problem.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007536
    DOI: 10.1016/j.amc.2022.127685
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322007536
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127685?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Hiroyuki Sato, 2023. "Riemannian optimization on unit sphere with p-norm and its applications," Computational Optimization and Applications, Springer, vol. 85(3), pages 897-935, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Hiroyuki Sato, 2023. "Riemannian optimization on unit sphere with p-norm and its applications," Computational Optimization and Applications, Springer, vol. 85(3), pages 897-935, July.
    5. 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.
    6. Xiaojing Zhu & Hiroyuki Sato, 2020. "Riemannian conjugate gradient methods with inverse retraction," Computational Optimization and Applications, Springer, vol. 77(3), pages 779-810, December.
    7. Xiaojing Zhu, 2017. "A Riemannian conjugate gradient method for optimization on the Stiefel manifold," Computational Optimization and Applications, Springer, vol. 67(1), pages 73-110, May.
    8. Lei Wang & Xin Liu & Yin Zhang, 2023. "A communication-efficient and privacy-aware distributed algorithm for sparse PCA," Computational Optimization and Applications, Springer, vol. 85(3), pages 1033-1072, July.
    9. Hiroyuki Sato & Kensuke Aihara, 2019. "Cholesky QR-based retraction on the generalized Stiefel manifold," Computational Optimization and Applications, Springer, vol. 72(2), pages 293-308, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007536. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.