# Preconditioned ADMM with nonlinear operator constraint

arXiv: https://arxiv.org/abs/1511.00425 · HTML: https://mlsanity.com/paper/1511.00425/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2015.

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

- [Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior](https://mlsanity.com/paper/2103.01648/) (2021)
- [Coefficient Shape Alignment in Multiple Functional Linear Regression](https://mlsanity.com/paper/2312.01925/) (2023)
- [ERD: Exponential Retinex decomposition based on weak space and hybrid nonconvex regularization and its denoising application](https://mlsanity.com/paper/2407.08498/) (2024)

## Abstract (arXiv)

We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging (MRI).