Safe Peeling for $\ell_{0}$-Regularized Least-Squares

We introduce a new methodology dubbed “safe peeling” to accelerate the resolution of
$\ell_{0}$
-regularized least-squares problems via a Branch-and-Bound (BnB) algorithm. Our procedure enables to tighten the convex relaxation considered at each node of the BnB decision tree and therefore potentially allows for more aggressive pruning. Numerical simulations show that our proposed methodology leads to significant gains in terms of number of nodes explored and overall solving time.