Screen & Relax: Accelerating The Resolution Of Elastic-Net By Safe Identification of The Solution Support

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 at identifying 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.