The Lawson-Hanson algorithm with deviation maximization: Finite convergence and sparse recovery

The Lawson-Hanson with Deviation Maximization (LHDM) method is a block algorithm for the solution of NonNegative Least Squares (NNLS) problems. In this work we devise an improved version of LHDM and we show that it terminates in a finite number of steps, unlike the previous version, originally developed for a special class of matrices. Moreover, we are concerned with finding sparse solutions of underdetermined linear systems by means of NNLS. An extensive campaign of experiments is performed in order to evaluate the performance gain with respect to the standard Lawson-Hanson algorithm. We also show the ability of LHDM to retrieve sparse solutions, comparing it against several ${\ell }_1$-minimization solvers in terms of solution quality and time-to-solution on a large set of dense instances.