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

TL;DR

This paper compares various reweighted l1-algorithms, including new variants, for solving cardinality minimization problems, highlighting how parameter choices influence performance through extensive numerical experiments.

Contribution

It introduces new reweighted l1-methods based on concave approximations of the l0-norm and compares their effectiveness with existing algorithms.

Findings

Reweighted l1-methods are effective for cardinality minimization.

Parameter changes significantly impact algorithm performance.

Numerical experiments validate the efficiency of reweighted l1 approaches.

Abstract

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.