Safe screening tests for lasso based on firmly non-expansiveness

International audience; This paper focusses on safe screening techniques for the LASSO problem. We derive a new sphere test, coined RFNE, exploiting the firmly non-expansiveness of projection operators. Our test generalizes some methods of the literature but, unlike the latter, exploits approximated primal-dual solutions of the LASSO problem while remaining safe and effective. Our simulation results show that the proposed RFNE test out-performs the best methodology of the state of the art, namely the GAP test derived by Fercoq et al.