  In this paper we propose a methodology to accelerate the resolution of the
so-called "Sorted L-One Penalized Estimation" (SLOPE) problem. Our method
leverages the concept of "safe screening", well-studied in the literature for
\textit{group-separable} sparsity-inducing norms, and aims at identifying the
zeros in the solution of SLOPE. More specifically, we derive a set of
\(\tfrac{n(n+1)}{2}\) inequalities for each element of the \(n\)-dimensional
primal vector and prove that the latter can be safely screened if some subsets
of these inequalities are verified. We propose moreover an efficient algorithm
to jointly apply the proposed procedure to all the primal variables. Our
procedure has a complexity \(\mathcal{O}(n\log n + LT)\) where \(T\leq n\) is a
problem-dependent constant and \(L\) is the number of zeros identified by the
tests. Numerical experiments confirm that, for a prescribed computational
budget, the proposed methodology leads to significant improvements of the
solving precision.
