# Approximate message-passing for convex optimization with non-separable penalties

arXiv: https://arxiv.org/abs/1809.06304 · HTML: https://mlsanity.com/paper/1809.06304/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2018.

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

- [Time-Embedded Algorithm Unrolling for Computational MRI](https://mlsanity.com/paper/2510.16321/) (2025)
- [Fast ℓ1-Regularized EEG Source Localization Using Variable Projection](https://mlsanity.com/paper/2502.20304/) (2025)
- [Optimizing Binary Symptom Checkers via Approximate Message Passing](https://mlsanity.com/paper/2111.00303/) (2021)

## Abstract (arXiv)

We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm. Specifically, the penalties we approach are convex on a linear transformation of the variable to be determined, a notable example being total variation (TV). We describe the connection between message-passing algorithms -- typically used for approximate inference -- and proximal methods for optimization, and show that our scheme is, as VAMP, similar in nature to the Peaceman-Rachford splitting, with the important difference that stepsizes are set adaptively. Finally, we benchmark the performance of our VAMP-like iteration in problems where TV penalties are useful, namely classification in task fMRI and reconstruction in tomography, and show faster convergence than that of state-of-the-art approaches such as FISTA and ADMM in most settings.