# Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

arXiv: https://arxiv.org/abs/1702.01850 · HTML: https://mlsanity.com/paper/1702.01850/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2017.

## Built on by (most cited first, 3 of 3)

- [Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraints](https://mlsanity.com/paper/2311.09065/) (2023)
- [First-order Methods for Affinely Constrained Composite Non-convex Non-smooth Problems: Lower Complexity Bound and Near-optimal Methods](https://mlsanity.com/paper/2307.07605/) (2023)
- [Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization](https://mlsanity.com/paper/2606.28307/) (2026)

## Abstract (arXiv)

This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the inclusion of an over-relaxation stepsize parameter belonging to the interval (0,2). To the best of our knowledge, all related papers in the literature only consider the case where the over-relaxation parameter lies in the interval (0,(1+√5)/2).