Necessary and sufficient conditions for noiseless sparse recovery via convex quadratic splines

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buir.contributor.authorPınar, Mustafa Ç.
dc.citation.epage209en_US
dc.citation.issueNumber1en_US
dc.citation.spage194en_US
dc.citation.volumeNumber40en_US
dc.contributor.authorPınar, Mustafa Ç.en_US
dc.date.accessioned2020-02-10T07:40:11Z
dc.date.available2020-02-10T07:40:11Z
dc.date.issued2019
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractThe problem of exact recovery of an individual sparse vector using the Basis Pursuit (BP) model is considered. A differentiable Huber loss function (a convex quadratic spline) is used to replace the $\ell_1$-norm in the BP model. Using the theory of duality and classical results from quadratic perturbation of linear programs, a necessary condition for exact recovery leading to a negative result is given. An easily verifiable sufficient condition is also presented.en_US
dc.description.provenanceSubmitted by Zeynep Aykut (zeynepay@bilkent.edu.tr) on 2020-02-10T07:40:11Z No. of bitstreams: 1 Necessary_and_sufficient_conditions_for_noiseless_sparse_recovery_via_convex_quadratic_splines.pdf: 366517 bytes, checksum: 97bb092bfc9d102b8b6515c7be7ecc42 (MD5)en
dc.description.provenanceMade available in DSpace on 2020-02-10T07:40:11Z (GMT). No. of bitstreams: 1 Necessary_and_sufficient_conditions_for_noiseless_sparse_recovery_via_convex_quadratic_splines.pdf: 366517 bytes, checksum: 97bb092bfc9d102b8b6515c7be7ecc42 (MD5) Previous issue date: 2019en
dc.identifier.doi10.1137/18M1185375en_US
dc.identifier.issn0895-4798
dc.identifier.urihttp://hdl.handle.net/11693/53208
dc.language.isoEnglishen_US
dc.publisherSociety for Industrial and Applied Mathematics Publicationsen_US
dc.relation.isversionofhttps://dx.doi.org/10.1137/18M1185375en_US
dc.source.titleSIAM Journal on Matrix Analysis and Applicationsen_US
dc.subjectExact recovery of a sparse vectoren_US
dc.subjectBasis pursuiten_US
dc.subjectHuber loss functionen_US
dc.subjectStrictly convex quadratic programmingen_US
dc.subjectLinear programmingen_US
dc.subjectConvex quadratic splinesen_US
dc.subjectℓ1-normen_US
dc.subjectQuadratic perturbationen_US
dc.titleNecessary and sufficient conditions for noiseless sparse recovery via convex quadratic splinesen_US
dc.typeArticleen_US

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