# Douglas--Rachford Splitting and ADMM for Pathological Convex Optimization

arXiv: https://arxiv.org/abs/1801.06618 · HTML: https://mlsanity.com/paper/1801.06618/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2018.

## Built on by (most cited first, 1 of 1)

- [Bregman Douglas-Rachford Splitting Method](https://mlsanity.com/paper/2509.08739/) (2025)

## Abstract (arXiv)

Despite the vast literature on DRS and ADMM, there has been very little work analyzing their behavior under pathologies. Most analyses assume a primal solution exists, a dual solution exists, and strong duality holds. When these assumptions are not met, i.e., under pathologies, the theory often breaks down and the empirical performance may degrade significantly. In this paper, we establish that DRS only requires strong duality to work, in the sense that asymptotically iterates are approximately feasible and approximately optimal.