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We introduce a new methodology dubbed ``safe peeling'' to accelerate theresolution of L0-regularized least-squares problems via a Branch-and-Bound(BnB) algorithm. Our procedure enables to tighten the convex relaxationconsidered at each node of the BnB decision tree and therefore potentiallyallows for more aggressive pruning. Numerical simulations show that ourproposed methodology leads to significant gains in terms of number of nodesexplored and overall solving time.s show that our proposed methodology leads tosignificant gains in terms of number of nodes explored and overall solvingtime.

Safe Peeling for L0-Regularized Least-Squares with supplementary material