IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v239y2026icp679-695.html

A modified Riemannian hybrid conjugate gradient method for nonconvex optimization problems

Author

Listed:
  • Wang, Yun
  • Bian, Yicong
  • Shao, Hu

Abstract

This paper proposes a new Riemannian hybrid conjugate gradient method aimed at solving nonconvex optimization problems on Riemannian manifolds. We extend the modified PRP and HS methods (WYL and VHS methods) to Riemannian manifolds, and introduce a new hybrid parameter that ensures the search direction always satisfies the descent property without requiring any line search. The global convergence of the method is established under the Riemannian weak Wolfe conditions. Finally, through numerical comparison with existing Riemannian conjugate gradient methods on five test problems, we validate the effectiveness of the proposed method.

Suggested Citation

  • Wang, Yun & Bian, Yicong & Shao, Hu, 2026. "A modified Riemannian hybrid conjugate gradient method for nonconvex optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 679-695.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:679-695
    DOI: 10.1016/j.matcom.2025.07.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475425002927
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.07.026?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

    for a different version of it.

    References listed on IDEAS

    as
    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 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.
    3. 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.
    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.
    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. 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. Shahabeddin Najafi & Masoud Hajarian, 2025. "A Globally Convergent Riemannian Memory Gradient Method," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-17, August.
    3. 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).
    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.
    5. 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.
    6. 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.
    7. 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.
    8. Elena Tovbis & Vladimir Krutikov & Predrag Stanimirović & Vladimir Meshechkin & Aleksey Popov & Lev Kazakovtsev, 2023. "A Family of Multi-Step Subgradient Minimization Methods," Mathematics, MDPI, vol. 11(10), pages 1-24, May.
    9. Serge Gratton & Vincent Malmedy & Philippe Toint, 2012. "Using approximate secant equations in limited memory methods for multilevel unconstrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 967-979, April.
    10. 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.
    11. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram & Ravina Sharma, 2023. "A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems," Mathematics, MDPI, vol. 11(23), pages 1-14, December.
    12. Priester, C. Robert & Melbourne-Thomas, Jessica & Klocker, Andreas & Corney, Stuart, 2017. "Abrupt transitions in dynamics of a NPZD model across Southern Ocean fronts," Ecological Modelling, Elsevier, vol. 359(C), pages 372-382.
    13. Ahmad M. Alshamrani & Adel Fahad Alrasheedi & Khalid Abdulaziz Alnowibet & Salem Mahdi & Ali Wagdy Mohamed, 2022. "A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization Problems," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    14. Xiaojing Zhu & Hiroyuki Sato, 2020. "Riemannian conjugate gradient methods with inverse retraction," Computational Optimization and Applications, Springer, vol. 77(3), pages 779-810, December.
    15. B. Sellami & Y. Chaib, 2016. "A new family of globally convergent conjugate gradient methods," Annals of Operations Research, Springer, vol. 241(1), pages 497-513, June.
    16. Neculai Andrei, 2013. "Another Conjugate Gradient Algorithm with Guaranteed Descent and Conjugacy Conditions for Large-scale Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 159-182, October.
    17. N. Andrei, 2009. "Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 249-264, May.
    18. Jose Giovany Babativa-Márquez & José Luis Vicente-Villardón, 2021. "Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    19. Chen, Kangming & Fukuda, Ellen Hidemi & Sato, Hiroyuki, 2025. "Nonlinear conjugate gradient method for vector optimization on Riemannian manifolds with retraction and vector transport," Applied Mathematics and Computation, Elsevier, vol. 486(C).
    20. Shuai Wang & Xiaoliang Wang & Yuzhu Tian & Liping Pang, 2024. "A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems," Mathematics, MDPI, vol. 12(19), pages 1-16, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:matcom:v:239:y:2026:i:c:p:679-695. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.