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

Abstract

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.

28 pages, 2 figures

References in corpus (4)

• Projected Subgradient Methods for Learning Sparse Gaussians
• A Fast Active Set Block Coordinate Descent Algorithm for ${\ell }_1$-regularized least squares
• An Active Set Algorithm for Nonlinear Optimization with Polyhedral Constraints
• A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables