New Results on Superlinear Convergence of Classical Quasi-Newton Methods

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.

J Optim Theory Appl (2021). arXiv admin note: text overlap with arXiv:2003.09174

References in corpus (3)

• Rates of superlinear convergence for classical quasi-Newton methods
• New Results on Superlinear Convergence of Classical Quasi-Newton Methods
• Non-asymptotic Superlinear Convergence of Standard Quasi-Newton Methods

Cited by in corpus (7)

• New Results on Superlinear Convergence of Classical Quasi-Newton Methods
• Explicit Convergence Rates of Greedy and Random Quasi-Newton Methods
• Explicit Superlinear Convergence Rates of Broyden's Methods in Nonlinear Equations
• Greedy and Random Broyden's Methods with Explicit Superlinear Convergence Rates in Nonlinear Equations
• A trust region-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization
• Hybrid Acceleration Scheme for Variance Reduced Stochastic Optimization Algorithms
• Quasi-Newton Methods for Saddle Point Problems and Beyond