Minimizers of sparsity regularized huber loss function
Date
2020Source Title
Journal of Optimization Theory and Applications
Print ISSN
0022-3239
Publisher
Springer
Volume
187
Issue
1
Pages
205 - 233
Language
English
Type
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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.