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An adaptive regularized proximal Newton-type methods for composite optimization over the Stiefel manifold

Author

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  • Qinsi Wang

    (Fudan University)

  • Wei Hong Yang

    (Fudan University)

Abstract

Recently, the proximal Newton-type method and its variants have been generalized to solve composite optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. In this paper, we propose an adaptive quadratically regularized proximal quasi-Newton method, named ARPQN, to solve this class of problems. Under some mild assumptions, the global convergence, the local linear convergence rate and the iteration complexity of ARPQN are established. Numerical experiments and comparisons with other state-of-the-art methods indicate that ARPQN is very promising. We also propose an adaptive quadratically regularized proximal Newton method, named ARPN. It is shown the ARPN method has a local superlinear convergence rate under certain reasonable assumptions, which demonstrates attractive convergence properties of regularized proximal Newton methods.

Suggested Citation

  • Qinsi Wang & Wei Hong Yang, 2024. "An adaptive regularized proximal Newton-type methods for composite optimization over the Stiefel manifold," Computational Optimization and Applications, Springer, vol. 89(2), pages 419-457, November.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:2:d:10.1007_s10589-024-00595-3
    DOI: 10.1007/s10589-024-00595-3
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    References listed on IDEAS

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    1. Geovani N. GRAPIGLIA & Yurii NESTEROV, 2017. "Regularized Newton methods for minimizing functions with Hölder continuous Hessians," LIDAM Reprints CORE 2846, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    3. Geovani N. Grapiglia & Yurii Nesterov, 2019. "Accelerated regularized Newton methods for minimizing composite convex functions," LIDAM Reprints CORE 3058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Hiva Ghanbari & Katya Scheinberg, 2018. "Proximal quasi-Newton methods for regularized convex optimization with linear and accelerated sublinear convergence rates," Computational Optimization and Applications, Springer, vol. 69(3), pages 597-627, April.
    5. Wen Huang & Ke Wei, 2023. "An inexact Riemannian proximal gradient method," Computational Optimization and Applications, Springer, vol. 85(1), pages 1-32, May.
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