On the performance of algorithms for the minimization of l1-penalized functionals

The problem of assessing the performance of algorithms used for the minimization of an l(1)-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of 'approximation isochrones' is introduced. Five different iterative minimization algorithms are tested and compared, as well as two warm-start strategies. Both well-conditioned and ill-conditioned problems are used in the comparison, and the contrast between these two categories is highlighted.