Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/23856
DC FieldValueLanguage
dc.contributorDepartment of Applied Mathematics-
dc.creatorChen, X-
dc.creatorGe, D-
dc.creatorWang, Z-
dc.creatorYe, Y-
dc.date.accessioned2014-12-19T06:53:34Z-
dc.date.available2014-12-19T06:53:34Z-
dc.identifier.issn0025-5610-
dc.identifier.urihttp://hdl.handle.net/10397/23856-
dc.language.isoenen_US
dc.subjectBridge estimatoren_US
dc.subjectNonconvex optimizationen_US
dc.subjectNonsmooth optimizationen_US
dc.subjectSparse solution reconstructionen_US
dc.subjectVariable selectionen_US
dc.titleComplexity of unconstrained L2-Lp minimizationen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage371-
dc.identifier.epage383-
dc.identifier.volume143-
dc.identifier.issue1-2-
dc.identifier.doi10.1007/s10107-012-0613-0-
dcterms.abstractWe consider the unconstrained Lq - Lp minimization: find a minimizer of ∥Ax-b∥q q+λ∥x∥ p p for given A ∈ Rm×n and parameters λ >0, p ∈[0, 1) and q≥ 1. This problem has been studied extensively in many areas. Especially, for the case when q=2, this problem is known as the L2-Lp minimization problem and has found its applications in variable selection problems and sparse least squares fitting for high dimensional data. Theoretical results show that the minimizers of the Lq - Lp problem have various attractive features due to the concavity and non-Lipschitzian property of the regularization function ∥̇∥p p. In this paper, we show that the L q - Lp minimization problem is strongly NP-hard for any p ∈ [0,1) and q≥ 1, including its smoothed version. On the other hand, we show that, by choosing parameters (p,λ) carefully, a minimizer, global or local, will have certain desired sparsity. We believe that these results provide new theoretical insights to the studies and applications of the concave regularized optimization problems.-
dcterms.bibliographicCitationMathematical programming, 2014, v. 143, no. 1-2, p. 371-383-
dcterms.isPartOfMathematical Programming-
dcterms.issued2014-
dc.identifier.scopus2-s2.0-84895059090-
dc.identifier.rosgroupidr69012-
dc.description.ros2013-2014 > Academic research: refereed > Publication in refereed journal-
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