Akkaya, Deniz2021-08-092021-08-092021-062021-062021-07-07http://hdl.handle.net/11693/76413Cataloged from PDF version of article.Thesis (Master's): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2021.Includes bibliographical references (leaves 52-54).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.viii, 57 leaves : charts ; 30 cm.Englishinfo:eu-repo/semantics/openAccessSparse solution of linear systemsRegularizationLocal minimizerGlobal mini-mizerHuber loss functionL1-normL0-normThesisB159354