Browsing by Subject "Global minimizer"
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Item Open Access Minimizers of sparsity regularized huber loss function(Springer, 2020) Akkaya, Deniz; Pınar, Mustafa Ç.We 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.