Akkaya, DenizPınar, Mustafa Ç.2021-02-192021-02-1920200022-3239http://hdl.handle.net/11693/75483We investigate the structure of the local and global minimizers of the Huber loss function regularized with a sparsity inducing L0 norm term. We characterize local minimizers and establish conditions that are necessary and sufficient for a local minimizer to be strict. A necessary condition is established for global minimizers, as well as non-emptiness of the set of global minimizers. The sparsity of minimizers is also studied by giving bounds on a regularization parameter controlling sparsity. Results are illustrated in numerical examples.EnglishSparse solution of linear systemsRegularizationLocal minimizerGlobal minimizerArticle10.1007/s10957-020-01745-3