# A Three-Operator Splitting Scheme Derived from Three-Block ADMM

arXiv: https://arxiv.org/abs/2411.00166 · HTML: https://mlsanity.com/paper/2411.00166/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2024.

## Built on by (most cited first, 2 of 2)

- [Finding Structure in Continual Learning](https://mlsanity.com/paper/2602.04555/) (2026)
- [Task Switching Without Forgetting via Proximal Decoupling](https://mlsanity.com/paper/2604.18857/) (2026)

## Abstract (arXiv)

This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems involving three operators. For solving a composite convex minimization of a sum of three functions, its formula resembles but is different from Davis-Yin splitting and the dual formulation of the classical three-block ADMM. Numerical tests suggest that such a splitting scheme is robust in the sense of allowing larger step sizes. When two functions have orthogonal domains, the splitting operator can be proven 1/2-averaged, which implies convergence of the iteration scheme using any positive step size.