Browsing by Subject "Sparse solution of linear systems"

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    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.
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    Minimizers of sparsity regularized robust loss functions
    (2021-06) Akkaya, Deniz
    We study the structure of the local and global minimizers of the Huber loss and the sum of absolute deviations functions regularized with a sparsity penalty L0 norm term. We char-acterize local minimizers for both loss functions, and establish conditions that are necessary and sufficient for local minimizers 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.