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A Nonmonotone Trust Region Method for Unconstrained Optimization Problems on Riemannian Manifolds

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Abstract

We propose a nonmonotone trust region method for unconstrained optimization problems on Riemannian manifolds. Global convergence to the first-order stationary points is proved under some reasonable conditions. We also establish local R-linear, super-linear and quadratic convergence rates. Preliminary experiments show that the algorithm is efficient.

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Acknowledgements

The authors thank the editors and referees for their constructive comments. X. Li was supported by the Young Scientists Fund of the National Natural Science Foundation of China (11901485). X. Wang was supported by the Natural Sciences and Engineering Research Council of Canada. M. Krishan Lal was supported by the UBC-SERB PhD fellowship.

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Authors and Affiliations

  1. School of Sciences and Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu, People’s Republic of China

    Xiaobo Li

  2. University of British Columbia Okanagan, Kelowna, Canada

    Xianfu Wang & Manish Krishan Lal

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  1. Xiaobo Li
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  2. Xianfu Wang
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  3. Manish Krishan Lal
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Correspondence to Xianfu Wang.

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Communicated by Alexandru Kristály.

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Li, X., Wang, X. & Krishan Lal, M. A Nonmonotone Trust Region Method for Unconstrained Optimization Problems on Riemannian Manifolds. J Optim Theory Appl 188, 547–570 (2021). https://doi.org/10.1007/s10957-020-01796-6

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  • DOI: https://doi.org/10.1007/s10957-020-01796-6

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