  The l1-ball is a nicely structured feasible set that is widely used in many
fields (e.g., machine learning, statistics and signal analysis) to enforce some
sparsity in the model solutions. In this paper, we devise an active-set
strategy for efficiently dealing with minimization problems over the l1-ball
and embed it into a tailored algorithmic scheme that makes use of a
non-monotone first-order approach to explore the given subspace at each
iteration. We prove global convergence to stationary points. Finally, we report
numerical experiments, on two different classes of instances, showing the
effectiveness of the algorithm.
