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

Safe rules for the identification of zeros in the solutions of the SLOPE problem