# Maximal Solutions of Sparse Analysis Regularization

arXiv: https://arxiv.org/abs/1703.00192 · HTML: https://mlsanity.com/paper/1703.00192/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [A Unified Framework for Pattern Recovery in Penalized and Thresholded Estimation and its Geometry](https://mlsanity.com/paper/2307.10158/) (2023)

## Abstract (arXiv)

This paper deals with the non-uniqueness of the solutions of an analysis-Lasso regularization. Most of previous works in this area is concerned with the case where the solution set is a singleton, or to derive guarantees to enforce uniqueness. Our main contribution consists in providing a geometrical interpretation of a solution with a maximal D-support, namely the fact that such a solution lives in the relative interior of the solution set. With this result in hand, we also provide a way to exhibit a maximal solution using a primal-dual interior point algorithm.