# Screen & Relax: Accelerating the resolution of Elastic-net by safe identification of the solution support

arXiv: https://arxiv.org/abs/2110.07281 · HTML: https://mlsanity.com/paper/2110.07281/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces with supplementary material](https://mlsanity.com/paper/2203.00987/) (2022)
- [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 procedure to accelerate the resolution of the well-known "Elastic-Net" problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a problem of reduced dimension. The identification of the support leverages the novel concept of "safe relaxing" where one aims to identify non-zero coefficients of the solution. It can be viewed as a dual approach to "safe screening" introduced in the last decade and allowing to reduce the problem dimension using the identification of zero coefficients of the solution. We show numerically that combining both methodologies in a "Screen & Relax" strategy enables to significantly improve the tradeoff between complexity and accuracy achievable by standard resolution techniques.