# AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization

arXiv: https://arxiv.org/abs/2401.08024 · HTML: https://mlsanity.com/paper/2401.08024/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2024.

## Built on by (most cited first, 8 of 8)

- [Projected gradient methods for nonconvex and stochastic smooth optimization: new complexities and auto-conditioned stepsizes](https://mlsanity.com/paper/2412.14291/) (2024)
- [Adaptive proximal gradient methods are universal without approximation](https://mlsanity.com/paper/2402.06271/) (2024)
- [Sparse Polyak: an adaptive step size rule for high-dimensional M-estimation](https://mlsanity.com/paper/2509.09802/) (2025)
- [Safeguarding adaptive methods: global convergence of Barzilai-Borwein and other stepsize choices](https://mlsanity.com/paper/2404.09617/) (2024)
- [AutoGD: Automatic Learning Rate Selection for Gradient Descent](https://mlsanity.com/paper/2510.09923/) (2025)
- [Adaptive Decentralized Composite Optimization via Three-Operator Splitting](https://mlsanity.com/paper/2602.17545/) (2026)
- [Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension n≥ 4](https://mlsanity.com/paper/2607.21579/) (2026)
- [Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size](https://mlsanity.com/paper/2608.12009/) (2026)

## Abstract (arXiv)

In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and essentially provides a convergent variant of the Barzilai-Borwein method for general unconstrained convex optimization. We analyze the ergodic convergence of the objective function value and the convergence of the iterates for solving general unconstrained convex optimization. Compared with existing works along this line of research, our algorithm gives the best lower bounds on the stepsize and the average of the stepsizes. Moreover, we present an extension of the proposed algorithm for solving composite optimization where the objective function is the summation of a smooth function and a nonsmooth function. Our numerical results also demonstrate very promising potential of the proposed algorithms on some representative examples.