Node-screening tests for L0-penalized least-squares problem with supplementary material

TL;DR

This paper introduces a new screening method for efficiently pruning nodes in branch-and-bound algorithms solving l0-penalized least-squares problems, significantly reducing computation time by safely discarding irrelevant nodes.

Contribution

It proposes two simple, low-cost tests for safe node screening in branch-and-bound algorithms, extending safe screening concepts to l0-penalized regression problems.

Findings

The screening tests effectively prune irrelevant nodes.

The methods reduce overall optimization time.

They leverage nesting properties for computational efficiency.

Abstract

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.