  Leveraging on the convexity of the Lasso problem , screening rules help in
accelerating solvers by discarding irrelevant variables, during the
optimization process. However, because they provide better theoretical
guarantees in identifying relevant variables, several non-convex regularizers
for the Lasso have been proposed in the literature. This work is the first that
introduces a screening rule strategy into a non-convex Lasso solver. The
approach we propose is based on a iterative majorization-minimization (MM)
strategy that includes a screening rule in the inner solver and a condition for
propagating screened variables between iterations of MM. In addition to improve
efficiency of solvers, we also provide guarantees that the inner solver is able
to identify the zeros components of its critical point in finite time. Our
experimental analysis illustrates the significant computational gain brought by
the new screening rule compared to classical coordinate-descent or proximal
gradient descent methods.
