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