Minimization over the l1-ball using an active-set non-monotone projected gradient

The l(1)-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 l(1)-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.

Automated summary

This paper introduces an active-set strategy for minimizing problems over the l(1)-ball, combined with a non-monotone first-order approach, proving global convergence to stationary points and demonstrating the effectiveness of the algorithm through numerical experiments.