# Block BFGS Methods

arXiv: https://arxiv.org/abs/1609.00318 · HTML: https://mlsanity.com/paper/1609.00318/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2016.

## Built on by (most cited first, 3 of 3)

- [Globally Convergent Multilevel Training of Deep Residual Networks](https://mlsanity.com/paper/2107.07572/) (2021)
- [Incremental Quasi-Newton Methods with Faster Superlinear Convergence Rates](https://mlsanity.com/paper/2402.02359/) (2024)
- [Optimization Geometrodynamics: Variational Reduction and Interaction Curvature](https://mlsanity.com/paper/2607.06723/) (2026)

## Abstract (arXiv)

We introduce a quasi-Newton method with block updates called Block BFGS. We show that this method, performed with inexact Armijo-Wolfe line searches, converges globally and superlinearly under the same convexity assumptions as BFGS. We also show that Block BFGS is globally convergent to a stationary point when applied to non-convex functions with bounded Hessian, and discuss other modifications for non-convex minimization. Numerical experiments comparing Block BFGS, BFGS and gradient descent are presented.