# Forward-Backward Splitting with Bregman Distances

arXiv: https://arxiv.org/abs/1505.05198 · HTML: https://mlsanity.com/paper/1505.05198/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2015.

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

- [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)
- [Bregman Graph Neural Network](https://mlsanity.com/paper/2309.06645/) (2023)
- [Enhancing Continuous Domain Adaptation with Multi-Path Transfer Curriculum](https://mlsanity.com/paper/2402.16681/) (2024)
- [Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size](https://mlsanity.com/paper/2608.12009/) (2026)
- [A Bregman Proximal Viewpoint on Neural Operators](https://mlsanity.com/paper/2610.20120/) (2026)

## Abstract (arXiv)

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces, where new algorithms are obtained.