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New Results on Superlinear Convergence of Classical Quasi-Newton Methods

Author

Listed:
  • Anton Rodomanov

    (Catholic University of Louvain)

  • Yurii Nesterov

    (Catholic University of Louvain)

Abstract

We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result, we obtain a significant improvement in the currently known estimates of the convergence rates for these methods. In particular, we show that the corresponding rate of the Broyden–Fletcher–Goldfarb–Shanno method depends only on the product of the dimensionality of the problem and the logarithm of its condition number.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:3:d:10.1007_s10957-020-01805-8
    DOI: 10.1007/s10957-020-01805-8
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    Citations

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    Cited by:

    1. Elena Tovbis & Vladimir Krutikov & Lev Kazakovtsev, 2024. "Newtonian Property of Subgradient Method with Optimization of Metric Matrix Parameter Correction," Mathematics, MDPI, vol. 12(11), pages 1-27, May.
    2. 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.
    3. Vladimir Krutikov & Elena Tovbis & Predrag Stanimirović & Lev Kazakovtsev, 2023. "On the Convergence Rate of Quasi-Newton Methods on Strongly Convex Functions with Lipschitz Gradient," Mathematics, MDPI, vol. 11(23), pages 1-15, November.
    4. Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.

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