  The problem of assessing the performance of algorithms used for the
minimization of an $\ell_1$-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.
