The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. in signal/image processing and statistics. A standard tool for dealing with sparse recovery is the ℓ1-regularized least-squares approach that has recently attracted the attention of many researchers. In this paper, we describe a new version of the two-block nonlinear constrained Gauss- Seidel algorithm for solving ℓ1-regularized least-squares that at each step of the iteration process fixes some variables to zero according to a simple active-set strategy. We prove the global convergence of the new algorithm and we show its efficiency reporting the results of some preliminary numerical experiments.
M. Porcelli, F. Rinaldi, A variable fixing version of the two-block nonlinear constrained Gauss-Seidel algorithm for l1-regularized least-squares, Computational Optimization and Applications, 59:3 (2014), pp. 565-589.