# Fixing and extending some recent results on the ADMM algorithm

arXiv: https://arxiv.org/abs/1612.05057 · HTML: https://mlsanity.com/paper/1612.05057/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2016.

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

- [First-Order Methods for Convex Optimization](https://mlsanity.com/paper/2101.00935/) (2021)
- [Federated Learning Using Three-Operator ADMM](https://mlsanity.com/paper/2211.04152/) (2022)

## Abstract (arXiv)

We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM algorithm that is able to handle convex optimization problems involving an additional smooth function in its objective, and which is evaluated through its gradient. Moreover, in each iteration we allow the use of variable metrics, while the investigations are carried out in the setting of infinite dimensional Hilbert spaces. This algorithmic scheme is investigated from the point of view of its convergence properties.