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Reweighted l1-algorithms have attracted a lot of attention in the field ofapplied mathematics. A unified framework of such algorithms has been recentlyproposed by Zhao and Li. In this paper we construct a few new examples ofreweighted l1-methods. These functions are certain concave approximations ofthe l0-norm function. We focus on the numerical comparison between some new andexisting reweighted l1-algorithms. We show how the change of parameters inreweighted algorithms may affect the performance of the algorithms for findingthe solution of the cardinality minimization problem. In our experiments, theproblem data were generated according to different statistical distributions,and we test the algorithms on different sparsity level of the solution of theproblem. Our numerical results demonstrate that the reweighted l1-method is oneof the efficient methods for locating the solution of the cardinalityminimization problem.

Comparison of several reweighted l1-algorithms for solving cardinality minimization problems