On the performance of algorithms for the minimization of $\ell_1$-penalized functionals

Details On the performance of algorithms for the minimization of $\ell_1$-penalized functionals On the performance of algorithms for the minimization of $\ell_1$-penalized functionals

2007-10-22

arxiv.org/abs/0710.4082v3

Mathematics

Numerical Analysis

18 pages, 10 figures; v3: expanded version with an additional synthetic test problems

Scientific paper

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.

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