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 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.