Minimizers of Sparsity Regularized Huber Loss Function

Deniz Akkaya () and Mustafa Ç. Pınar ()
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Deniz Akkaya: Bilkent University
Mustafa Ç. Pınar: Bilkent University

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 1, No 10, 205-233

Abstract: Abstract 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.

Keywords: Sparse solution of linear systems; Regularization; local minimizer; Global minimizer; Huber loss function; L0-norm; 15A29; 62J05; 90C26; 90C46 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01745-3

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