Sparse solutions to an underdetermined system of linear equations via penalized Huber loss

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buir.contributor.authorPınar, Mustafa Çelebi
buir.contributor.orcidPınar, Mustafa Çelebi|0000-0002-8307-187X
dc.citation.epage1537en_US
dc.citation.issueNumber22en_US
dc.citation.spage1521en_US
dc.contributor.authorKızılkale, C.
dc.contributor.authorPınar, Mustafa Çelebi
dc.date.accessioned2021-03-10T09:03:14Z
dc.date.available2021-03-10T09:03:14Z
dc.date.issued2020
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractWe investigate the computation of a sparse solution to an underdetermined system of linear equations using the Huber loss function as a proxy for the 1-norm and a quadratic error term à la Lasso. The approach is termed “penalized Huber loss”. The results of the paper allow to calculate a sparse solution using a simple extrapolation formula under a sign constancy condition that can be removed if one works with extreme points. Conditions leading to sign constancy, as well as necessary and sufficient conditions for computation of a sparse solution by penalized Huber loss, and ties among different solutions are presented.en_US
dc.description.provenanceSubmitted by Zeynep Aykut (zeynepay@bilkent.edu.tr) on 2021-03-10T09:03:14Z No. of bitstreams: 1 Sparse_solutions_to_an_underdetermined_system_of_linear_equations_via_penalized_Huber_loss.pdf: 1505990 bytes, checksum: 2b778356b8cb4132dfdb32f420a6f7de (MD5)en
dc.description.provenanceMade available in DSpace on 2021-03-10T09:03:14Z (GMT). No. of bitstreams: 1 Sparse_solutions_to_an_underdetermined_system_of_linear_equations_via_penalized_Huber_loss.pdf: 1505990 bytes, checksum: 2b778356b8cb4132dfdb32f420a6f7de (MD5) Previous issue date: 2020en
dc.identifier.doi10.1007/s11081-020-09577-wen_US
dc.identifier.eissn1573-2924en_US
dc.identifier.issn1389-4420
dc.identifier.urihttp://hdl.handle.net/11693/75913
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttps://dx.doi.org/10.1007/s11081-020-09577-wen_US
dc.source.titleOptimization and Engineeringen_US
dc.subjectSparse solutionen_US
dc.subjectLinear system of equationsen_US
dc.subjectCompressed sensingen_US
dc.subjectBasis pursuiten_US
dc.subjectHuber loss functionen_US
dc.subjectConvex quadratic splinesen_US
dc.subjectLinear programmingen_US
dc.subjectl1-normen_US
dc.subjectQuadratic perturbationen_US
dc.subjectStrictly convex quadratic programmingen_US
dc.titleSparse solutions to an underdetermined system of linear equations via penalized Huber lossen_US
dc.typeArticleen_US

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