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Global convergence of Hager–Zhang type Riemannian conjugate gradient method

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  • 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
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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. 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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    Cited by:

    1. 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.

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