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Convergence Rate of Descent Method with New Inexact Line-Search on Riemannian Manifolds

Author

Listed:
  • Xiao-bo Li

    (Southwest Petroleum University)

  • Nan-jing Huang

    (Sichuan University)

  • Qamrul Hasan Ansari

    (Aligarh Muslim University
    King Fahd University of Petroleum and Minerals)

  • Jen-Chih Yao

    (China Medical University)

Abstract

In this paper, we propose the descent method with new inexact line-search for unconstrained optimization problems on Riemannian manifolds. The global convergence of the proposed method is established under some appropriate assumptions. We further analyze some convergence rates, namely R-linear convergence rate, superlinear convergence rate and quadratic convergence rate, of the proposed descent method.

Suggested Citation

  • Xiao-bo Li & Nan-jing Huang & Qamrul Hasan Ansari & Jen-Chih Yao, 2019. "Convergence Rate of Descent Method with New Inexact Line-Search on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 830-854, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1390-6
    DOI: 10.1007/s10957-018-1390-6
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    References listed on IDEAS

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    1. Y. Yang, 2007. "Globally Convergent Optimization Algorithms on Riemannian Manifolds: Uniform Framework for Unconstrained and Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 245-265, February.
    2. Xiao-bo Li & Li-wen Zhou & Nan-jing Huang, 2016. "Gap Functions and Global Error Bounds for Generalized Mixed Variational Inequalities on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 830-849, March.
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    Cited by:

    1. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "A Hybrid Forward–Backward Algorithm and Its Optimization Application," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
    2. Xiaobo Li & Xianfu Wang & Manish Krishan Lal, 2021. "A Nonmonotone Trust Region Method for Unconstrained Optimization Problems on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 547-570, February.
    3. Vo Minh Tam & Nguyen Hung & Zhenhai Liu & Jen Chih Yao, 2022. "Levitin–Polyak Well-Posedness by Perturbations for the Split Hemivariational Inequality Problem on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 684-706, November.

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