# Bregman Augmented Lagrangian and Its Acceleration

arXiv: https://arxiv.org/abs/2002.06315 · HTML: https://mlsanity.com/paper/2002.06315/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2020.

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

- [Proximal Point Imitation Learning](https://mlsanity.com/paper/2209.10968/) (2022)
- [Bregman Douglas-Rachford Splitting Method](https://mlsanity.com/paper/2509.08739/) (2025)
- [An inexact Bregman proximal point method and its acceleration version for unbalanced optimal transport](https://mlsanity.com/paper/2402.16978/) (2024)

## Abstract (arXiv)

We study the Bregman Augmented Lagrangian method (BALM) for solving convex problems with linear constraints. For classical Augmented Lagrangian method, the convergence rate and its relation with the proximal point method is well-understood. However, the convergence rate for BALM has not yet been thoroughly studied in the literature. In this paper, we analyze the convergence rates of BALM in terms of the primal objective as well as the feasibility violation. We also develop, for the first time, an accelerated Bregman proximal point method, that improves the convergence rate from O(1/sumk=0T-1ηk) to O(1/(sumk=0T-1√ηk)2), where ηkk=0T-1 is the sequence of proximal parameters. When applied to the dual of linearly constrained convex programs, this leads to the construction of an accelerated BALM, that achieves the improved rates for both primal and dual convergences.