# Bregman Forward-Backward Operator Splitting

arXiv: https://arxiv.org/abs/1908.03878 · HTML: https://mlsanity.com/paper/1908.03878/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2019.

## Built on by (most cited first, 7 of 7)

- [Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopes](https://mlsanity.com/paper/2207.04387/) (2022)
- [First-Order Methods for Convex Optimization](https://mlsanity.com/paper/2101.00935/) (2021)
- [A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimization](https://mlsanity.com/paper/2112.11928/) (2021)
- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [Enhancing Continuous Domain Adaptation with Multi-Path Transfer Curriculum](https://mlsanity.com/paper/2402.16681/) (2024)
- [Bregman Douglas-Rachford Splitting Method](https://mlsanity.com/paper/2509.08739/) (2025)
- [Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size](https://mlsanity.com/paper/2608.12009/) (2026)

## Abstract (arXiv)

We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far been proved only in the case of minimization problems. The proposed framework features Bregman distances that vary over the iterations and a novel assumption on the single-valued operator that captures various properties scattered in the literature. In the minimization setting, we obtain rates that are sharper than existing ones.