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

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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.

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Acknowledgements

Authors are grateful to the referees for their valuable suggestions and comments to improve this paper. In this paper, the second author was supported by the National Natural Science Foundation of China (11671282), the third author was supported by a research Grant of DST-SERB No. EMR/2016/005124 and the fourth author was partially supported by the Grant MOST 105-2115-M-039-002-MY3.

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Authors and Affiliations

  1. School of Sciences, Southwest Petroleum University, Chengdu, 610500, People’s Republic of China

    Xiao-bo Li

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China

    Nan-jing Huang

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari

  4. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Qamrul Hasan Ansari

  5. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Jen-Chih Yao

Authors
  1. Xiao-bo Li
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  2. Nan-jing Huang
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  3. Qamrul Hasan Ansari
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  4. Jen-Chih Yao
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Corresponding author

Correspondence to Qamrul Hasan Ansari.

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Communicated by Sándor Zoltán Németh.

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Li, Xb., Huang, Nj., Ansari, Q.H. et al. Convergence Rate of Descent Method with New Inexact Line-Search on Riemannian Manifolds. J Optim Theory Appl 180, 830–854 (2019). https://doi.org/10.1007/s10957-018-1390-6

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  • DOI: https://doi.org/10.1007/s10957-018-1390-6

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