IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v197y2023i3d10.1007_s10957-023-02227-y.html
   My bibliography  Save this article

An Adaptive Riemannian Gradient Method Without Function Evaluations

Author

Listed:
  • Geovani N. Grapiglia

    (Université catholique de Louvain, ICTEAM/INMA)

  • Gabriel F. D. Stella

    (Universidade Federal do Paraná, Centro Politécnico)

Abstract

In this paper, we present an adaptive gradient method for the minimization of differentiable functions on Riemannian manifolds. The method is designed to minimize functions with Lipschitz continuous gradient field, but it does not required the knowledge of the Lipschitz constant. In contrast with line search schemes, the dynamic adjustment of the stepsizes is done without the use of function evaluations. We prove worst-case complexity bounds for the number of gradient evaluations that the proposed method needs to find an approximate stationary point. Preliminary numerical results are also presented and illustrate the potential advantages of different versions of our method in comparison with a Riemannian gradient method with Armijo line search.

Suggested Citation

  • Geovani N. Grapiglia & Gabriel F. D. Stella, 2023. "An Adaptive Riemannian Gradient Method Without Function Evaluations," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1140-1160, June.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02227-y
    DOI: 10.1007/s10957-023-02227-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02227-y
    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/s10957-023-02227-y?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. Glaydston C. Bento & Orizon P. Ferreira & Jefferson G. Melo, 2017. "Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 548-562, May.
    Full references (including those not matched with items on IDEAS)

    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. Harry Oviedo, 2023. "Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold," Mathematics, MDPI, vol. 11(11), pages 1-17, May.
    2. Yldenilson Torres Almeida & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos de Oliveira Souza, 2020. "A modified proximal point method for DC functions on Hadamard manifolds," Computational Optimization and Applications, Springer, vol. 76(3), pages 649-673, July.
    3. Orizon P. Ferreira & Mauricio S. Louzeiro & Leandro F. Prudente, 2020. "Iteration-Complexity and Asymptotic Analysis of Steepest Descent Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 507-533, February.
    4. Dewei Zhang & Sam Davanloo Tajbakhsh, 2023. "Riemannian Stochastic Variance-Reduced Cubic Regularized Newton Method for Submanifold Optimization," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 324-361, January.

    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:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02227-y. 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: 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.