# An O(nlog(n)) Algorithm for Projecting Onto the Ordered Weighted ℓ1 Norm Ball

arXiv: https://arxiv.org/abs/1505.00870 · HTML: https://mlsanity.com/paper/1505.00870/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2015.

## Built on by (most cited first, 2 of 2)

- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Fast Computation of Superquantile-Constrained Optimization Through Implicit Scenario Reduction](https://mlsanity.com/paper/2405.07965/) (2024)

## Abstract (arXiv)

The ordered weighted ℓ1 (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm. This norm has desirable statistical properties and can be used to perform simultaneous clustering and regression. In this paper, we show how to compute the projection of an n-dimensional vector onto the OWL norm ball in O(nlog(n)) operations. In addition, we illustrate the performance of our algorithm on a synthetic regression test.