IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v64y2016i1d10.1007_s10589-015-9801-1.html
   My bibliography  Save this article

A Dai–Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions

Author

Listed:
  • Hiroyuki Sato

    (Tokyo University of Science)

Abstract

This article describes a new Riemannian conjugate gradient method and presents a global convergence analysis. The existing Fletcher–Reeves-type Riemannian conjugate gradient method is guaranteed to be globally convergent if it is implemented with the strong Wolfe conditions. On the other hand, the Dai–Yuan-type Euclidean conjugate gradient method generates globally convergent sequences under the weak Wolfe conditions. This article deals with a generalization of Dai–Yuan’s Euclidean algorithm to a Riemannian algorithm that requires only the weak Wolfe conditions. The global convergence property of the proposed method is proved by means of the scaled vector transport associated with the differentiated retraction. The results of numerical experiments demonstrate the effectiveness of the proposed algorithm.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9801-1
    DOI: 10.1007/s10589-015-9801-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-015-9801-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10589-015-9801-1?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.

    Citations

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


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Xiaojing Zhu & Hiroyuki Sato, 2020. "Riemannian conjugate gradient methods with inverse retraction," Computational Optimization and Applications, Springer, vol. 77(3), pages 779-810, December.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    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.
    10. 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.

    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:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9801-1. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.