A variable fixing version of the two-block nonlinear constrained Gauss-Seidel algorithm for l1-regularized least-squares

The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields like e.g. signal/image processing and statistics. A standard tool for dealing with sparse recovery is the l1-regularized least-squares approach that has been recently attracting 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 rule. We prove the global convergence of the method and we report numerical results on some test problems showing the efficiency of the implemented algorithm.