Maximal Solutions of Sparse Analysis Regularization
Optimization and Control
2017-03-02 v1
Abstract
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.
Cite
@article{arxiv.1703.00192,
title = {Maximal Solutions of Sparse Analysis Regularization},
author = {Abdessamad Barbara and Abderrahim Jourani and Samuel Vaiter},
journal= {arXiv preprint arXiv:1703.00192},
year = {2017}
}