  We present a novel screening methodology to safely discard irrelevant nodes
within a generic branch-and-bound (BnB) algorithm solving the l0-penalized
least-squares problem. Our contribution is a set of two simple tests to detect
sets of feasible vectors that cannot yield optimal solutions. This allows to
prune nodes of the BnB search tree, thus reducing the overall optimization
time. One cornerstone of our contribution is a nesting property between tests
at different nodes that allows to implement them with a low computational cost.
Our work leverages the concept of safe screening, well known for
sparsity-inducing convex problems, and some recent advances in this field for
l0-penalized regression problems.
