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      Minimizers of sparsity regularized huber loss function

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      Author(s)
      Akkaya, Deniz
      Pınar, Mustafa Ç.
      Date
      2020
      Source Title
      Journal of Optimization Theory and Applications
      Print ISSN
      0022-3239
      Publisher
      Springer
      Volume
      187
      Issue
      1
      Pages
      205 - 233
      Language
      English
      Type
      Article
      Item Usage Stats
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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.
      Keywords
      Sparse solution of linear systems
      Regularization
      Local minimizer
      Global minimizer
      Permalink
      http://hdl.handle.net/11693/75483
      Published Version (Please cite this version)
      https://dx.doi.org/10.1007/s10957-020-01745-3
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      • Department of Industrial Engineering 733
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