# Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces with supplementary material

arXiv: https://arxiv.org/abs/2203.00987 · HTML: https://mlsanity.com/paper/2203.00987/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 2 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Gap Safe screening rules for sparsity enforcing penalties](https://mlsanity.com/paper/1611.05780/) (2016)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [Screening Tests for Lasso Problems](https://mlsanity.com/paper/1405.4897/) (2014)
- [Safe Screening With Variational Inequalities and Its Application to LASSO](https://mlsanity.com/paper/1307.7577/) (2013)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Safe squeezing for antisparse coding](https://mlsanity.com/paper/1911.07508/) (2019)
- [Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares](https://mlsanity.com/paper/2102.04108/) (2021)
- [Screen & Relax: Accelerating the resolution of Elastic-net by safe identification of the solution support](https://mlsanity.com/paper/2110.07281/) (2021)

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

- [One to beat them all: "RYU" -- a unifying framework for the construction of safe balls](https://mlsanity.com/paper/2312.00640/) (2023)
- [Gap Safe Screening Rules for Fast Training of Robust Support Vector Machines under Feature Noise](https://mlsanity.com/paper/2603.25221/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel safe screening test for Lasso. Our procedure is based on a safe region with a dome geometry and exploits a canonical representation of the set of half-spaces (referred to as "dual cutting half-spaces" in this paper) containing the dual feasible set. The proposed safe region is shown to be always included in the state-of-the-art "GAP Sphere" and "GAP Dome" proposed by Fercoq et al. (and strictly so under very mild conditions) while involving the same computational burden. Numerical experiments confirm that our new dome enables to devise more powerful screening tests than GAP regions and lead to significant acceleration to solve Lasso.