# Nonconvex flexible sparsity regularization: theory and monotone numerical schemes

arXiv: https://arxiv.org/abs/2111.06281 · HTML: https://mlsanity.com/paper/2111.06281/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2021.

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

- [Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Framework](https://mlsanity.com/paper/2511.06235/) (2025)

## Abstract (arXiv)

Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and numerical perspectives. Namely, we show convergence of the regularization method and establish convergence properties of a couple of majorization approaches for the associated nonconvex problems. We also test a monotone algorithm for an academic example where the operator is an M matrix, and on a time-dependent optimal control problem, pointing out the advantages of employing variable penalties over a fixed penalty.