# Iteration-complexity of a Jacobi-type non-Euclidean ADMM for multi-block linearly constrained nonconvex programs

arXiv: https://arxiv.org/abs/1705.07229 · HTML: https://mlsanity.com/paper/1705.07229/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2017.

## Built on by (most cited first, 5 of 5)

- [A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization](https://mlsanity.com/paper/2102.05433/) (2021)
- [Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraints](https://mlsanity.com/paper/2311.09065/) (2023)
- [Block Majorization Minimization with Extrapolation and Application to β-NMF](https://mlsanity.com/paper/2401.06646/) (2024)
- [Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints](https://mlsanity.com/paper/2201.07657/) (2022)
- [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)

## Abstract (arXiv)

This paper establishes the iteration-complexity of a Jacobi-type non-Euclidean proximal alternating direction method of multipliers (ADMM) for solving multi-block linearly constrained nonconvex programs. The subproblems of this ADMM variant can be solved in parallel and hence the method has great potential to solve large scale multi-block linearly constrained nonconvex programs. Moreover, our analysis allows the Lagrange multiplier to be updated with a relaxation parameter in the interval (0, 2).