Comparison of several reweighted l1-algorithms for solving cardinality minimization problems
This work is incremental, focusing on parameter tuning and comparison for researchers in applied mathematics dealing with sparse optimization problems.
The paper tackled the cardinality minimization problem by constructing new reweighted l1-methods and comparing them with existing algorithms, showing that parameter changes affect performance and that reweighted l1-methods are efficient, with numerical results based on different statistical distributions and sparsity levels.
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.