# Decreasing Weighted Sorted ℓ1 Regularization

arXiv: https://arxiv.org/abs/1404.3184 · HTML: https://mlsanity.com/paper/1404.3184/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2014.

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

- [Efficient Solvers for SLOPE in R, Python, Julia, and C++](https://mlsanity.com/paper/2511.02430/) (2025)

## Abstract (arXiv)

We consider a new family of regularizers, termed it weighted sorted ℓ1 norms (WSL1), which generalizes the recently introduced it octagonal shrinkage and clustering algorithm for regression (OSCAR) and also contains the ℓ1 and ℓ∞ norms as particular instances. We focus on a special case of the WSL1, the sl decreasing WSL1 (DWSL1), where the elements of the argument vector are sorted in non-increasing order and the weights are also non-increasing. In this paper, after showing that the DWSL1 is indeed a norm, we derive two key tools for its use as a regularizer: the dual norm and the Moreau proximity operator.