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Convergence analysis of the DFP algorithm for unconstrained optimization problems on Riemannian manifolds

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Abstract

In this paper, we propose the DFP algorithm with inexact line search for unconstrained optimization problems on Riemannian manifolds. Under some reasonable conditions, the global convergence result is established and the superlinear local convergence rate of the DFP algorithm is proved on Riemannian manifolds. The preliminary computational experiment is also reported to illustrate the effectiveness of the DFP algorithm.

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Acknowledgements

The authors thank the editors and referees for their constructive comments. Xiaobo Li is supported by the Young Scientists Fund of the National Natural Science Foundation of China (No.11901485), Natural Science Foundation of Sichuan (No.2023NSFSC1354, No.2022NSFSC0532), the Fundamental Research Funds for the Central Universities (No. PHD2023-057). Kai Tu is supported by National Natural Science Foundation of China (No. 12101436) and the Humanities and Social Sciences Foundation of Ministry of Education of China (No. 23YJC630158). Jian Lu is supported by the National Natural Science Foundation of China under Grants 12271217, U21A20455, 61972265, 11871348; the Natural Science Foundation of Guangdong Province of China under Grant 2020B1515310008; in part by the Educational Commission of Guangdong Province of China under Grant 2019KZDZX1007.

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Authors and Affiliations

  1. School of Sciences, Civil Aviation Flight University of China, Guanghan, 618300, China

    Xiao-bo Li

  2. School of Mathematical Sciences, Shenzhen University, Shenzhen, 518060, China

    Kai Tu

  3. Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, 518060, China

    Jian Lu

  4. Pazhou Lab, Guangzhou, China

    Jian Lu

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  1. Xiao-bo Li
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  2. Kai Tu
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  3. Jian Lu
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Correspondence to Kai Tu.

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Li, Xb., Tu, K. & Lu, J. Convergence analysis of the DFP algorithm for unconstrained optimization problems on Riemannian manifolds. Optim Lett (2024). https://doi.org/10.1007/s11590-024-02103-2

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