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New Results on Superlinear Convergence of Classical Quasi-Newton Methods

Author

Listed:
  • Rodomanov, Anton

    (Université catholique de Louvain, ICTEAM)

  • Nesterov, Yurii

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

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

  • Rodomanov, Anton & Nesterov, Yurii, 2023. "New Results on Superlinear Convergence of Classical Quasi-Newton Methods," LIDAM Reprints CORE 3249, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3249
    DOI: https://doi.org/10.1007/s10957-020-01805-8
    Note: In: Journal of Optimization Theory and Applications, 2021, vol. 188(3), p. 744-769
    as

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