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Greedy PSB methods with explicit superlinear convergence

Author

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  • Zhen-Yuan Ji

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Yu-Hong Dai

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

Abstract

Recently, Rodomanov and Nesterov proposed a class of greedy quasi-Newton methods and established the first explicit local superlinear convergence result for Quasi-Newton type methods. In this paper, we study a variant of Powell-Symmetric-Broyden (PSB) updates based on the greedy strategy. Firstly, we give explicit condition-number-free superlinear convergence rates of proposed greedy PSB methods. Secondly, we prove the global convergence of greedy PSB methods by applying the trust-region framework. One advantage of this result is that the initial Hessian approximation can be chosen arbitrarily. Thirdly, we analyze the behaviour of the randomized PSB method, that selects the direction randomly from any spherical symmetry distribution. Finally, preliminary numerical experiments illustrate the efficiency of proposed PSB methods compared with the standard SR1 method and PSB method. Our results are given under the assumption that the objective function is a strongly convex function, and its gradient and Hessian are Lipschitz continuous.

Suggested Citation

  • Zhen-Yuan Ji & Yu-Hong Dai, 2023. "Greedy PSB methods with explicit superlinear convergence," Computational Optimization and Applications, Springer, vol. 85(3), pages 753-786, July.
    • Handle: RePEc:spr:coopap:v:85:y:2023:i:3:d:10.1007_s10589-023-00495-y
    DOI: 10.1007/s10589-023-00495-y
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    References listed on IDEAS

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    1. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, December.
    2. Anton Rodomanov & Yurii Nesterov, 2021. "New Results on Superlinear Convergence of Classical Quasi-Newton Methods," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 744-769, March.
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