# Fast projection onto the ordered weighted ℓ1 norm ball

arXiv: https://arxiv.org/abs/2002.05004 · HTML: https://mlsanity.com/paper/2002.05004/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

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

- [Fast Computation of Superquantile-Constrained Optimization Through Implicit Scenario Reduction](https://mlsanity.com/paper/2405.07965/) (2024)

## Abstract (arXiv)

In this paper, we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted ℓ1 (OWL1) norm ball. In particular, an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem. Global and local quadratic convergence results, as well as the finite termination property, of the algorithm are proved. Numerical comparisons with the two best-known methods demonstrate the efficiency of our method. In addition, we derive the generalized Jacobian of the studied projector which, we believe, is crucial for the future designing of fast second order nonsmooth methods for solving general OWL1 norm constrained problems.