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

TL;DR

This paper introduces a new method called 'Screen & Relax' that accelerates solving Elastic-Net problems by safely identifying non-zero coefficients, reducing problem size, and improving computational efficiency.

Contribution

The paper presents a novel 'safe relaxing' approach for identifying non-zero coefficients, enhancing existing screening methods to speed up Elastic-Net solutions.

Findings

Significant reduction in computation time for Elastic-Net problems.

Improved accuracy-complexity tradeoff over standard methods.

Effective combination of support screening and relaxing techniques.

Abstract

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.