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A modified Riemannian hybrid conjugate gradient method for nonconvex optimization problems

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  • 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
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    References listed on IDEAS

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    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. 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.
    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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    1. Nasiru Salihu & Poom Kumam & Sani Salisu & Kanokwan Sitthithakerngkiet, 2026. "On New Spectral Conjugate Gradient Methods for Riemannian Optimization Using Retraction and Scaled Vector Transport," SN Operations Research Forum, Springer, vol. 7(1), pages 1-34, March.

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