# Safeguarding adaptive methods: global convergence of Barzilai-Borwein and other stepsize choices

arXiv: https://arxiv.org/abs/2404.09617 · HTML: https://mlsanity.com/paper/2404.09617/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Adaptive Gradient Descent without Descent](https://mlsanity.com/paper/1910.09529/) (2019)
- [Adaptive Proximal Gradient Method for Convex Optimization](https://mlsanity.com/paper/2308.02261/) (2023)
- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)
- [Stabilized Barzilai-Borwein method](https://mlsanity.com/paper/1907.06409/) (2019)
- [AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization](https://mlsanity.com/paper/2401.08024/) (2024)
- [Adaptive proximal gradient methods are universal without approximation](https://mlsanity.com/paper/2402.06271/) (2024)
- [On a Faster R-Linear Convergence Rate of the Barzilai-Borwein Method](https://mlsanity.com/paper/2101.00205/) (2021)
- [On the convergence of adaptive first order methods: proximal gradient and alternating minimization algorithms](https://mlsanity.com/paper/2311.18431/) (2023)
- [Douglas-Rachford splitting and ADMM for nonconvex optimization: Accelerated and Newton-type linesearch algorithms](https://mlsanity.com/paper/2005.10230/) (2020)

## Abstract (arXiv)

Leveraging on recent advancements on adaptive methods for convex minimization problems, this paper provides a linesearch-free proximal gradient framework for globalizing the convergence of popular stepsize choices such as Barzilai-Borwein and one-dimensional Anderson acceleration. This framework can cope with problems in which the gradient of the differentiable function is merely locally H"older continuous. Our analysis not only encompasses but also refines existing results upon which it builds. The theory is corroborated by numerical evidence that showcases the synergetic interplay between fast stepsize selections and adaptive methods.