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New Results on Superlinear Convergence of Classical Quasi-Newton Methods

arXiv 2004.14866 ↗First posted 29 Apr 2020math.OCcited by 15

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Abstract (arXiv)

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.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Apr 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 3; 2023: 3; 2024: 1; 2025: 4; 2026: 1.

15 papers.

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  1. 2022Hessian Averaging in Stochastic Newton Methods Achieves Superlinear Convergencecited by 14
  2. 2022Second-order optimization with lazy Hessianscited by 13
  3. 2023Online Learning Guided Curvature Approximation: A Quasi-Newton Method with Global Non-Asymptotic Superlinear Convergencecited by 11
  4. 2021Quasi-Newton Methods for Saddle Point Problems and Beyondcited by 10
  5. 2022Optimization for Classical Machine Learning Problems on the GPUcited by 5
  6. 2023Accelerated Quasi-Newton Proximal Extragradient: Faster Rate for Smooth Convex Optimizationcited by 4
  7. 2021Approximate Newton policy gradient algorithmscited by 3
  8. 2024Multiple Greedy Quasi-Newton Methods for Saddle Point Problemscited by 3
  9. 2025Gradient Methods with Online Scaling Part I. Theoretical Foundationscited by 3
  10. 2025Gradient-Normalized Smoothness for Optimization with Approximate Hessianscited by 3
  11. 2021Exploiting Local Convergence of Quasi-Newton Methods Globally: Adaptive Sample Size Approachcited by 2
  12. 2025qNBO: quasi-Newton Meets Bilevel Optimizationcited by 2
3 more
  1. 2023Sharpened Lazy Incremental Quasi-Newton Methodcited by 1
  2. 2025Simple Stepsize for Quasi-Newton Methods with Global Convergence Guaranteescited by 0
  3. 2026Primal Acceleration of Newton's Methodcited by 0