Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/66842
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorChen, Xen_US
dc.creatorLu, Zen_US
dc.creatorPong, TKen_US
dc.date.accessioned2017-05-22T02:26:51Z-
dc.date.available2017-05-22T02:26:51Z-
dc.identifier.issn1052-6234en_US
dc.identifier.urihttp://hdl.handle.net/10397/66842-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2016 Society for Industrial and Applied Mathematicsen_US
dc.rightsThe following publication Chen, X., Lu, Z., & Pong, T. K. (2016). Penalty methods for a class of non-Lipschitz optimization problems. SIAM Journal on Optimization, 26(3), 1465-1492 is available at is available at https://doi.org/10.1137/15M1028054en_US
dc.subjectExact penaltyen_US
dc.subjectProximal gradient methoden_US
dc.subjectSparse solutionen_US
dc.subjectNonconvex optimizationen_US
dc.subjectNon-Lipschitz optimizationen_US
dc.titlePenalty methods for a class of non-Lipschitz optimization problemsen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage1465en_US
dc.identifier.epage1492en_US
dc.identifier.volume26en_US
dc.identifier.issue3en_US
dc.identifier.doi10.1137/15M1028054en_US
dcterms.abstractWe consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing sparsity in the solutions while the constraint set models the noise tolerance and incorporates other prior information for data fitting. To solve this class of constrained optimization problems, a common approach is the penalty method. However, there is little theory on exact penalization for problems with nonconvex and non-Lipschitz objective functions. In this paper, we study the existence of exact penalty parameters regarding local minimizers, stationary points, and $\epsilon$-minimizers under suitable assumptions. Moreover, we discuss a penalty method whose subproblems are solved via a nonmonotone proximal gradient method with a suitable update scheme for the penalty parameters and prove the convergence of the algorithm to a KKT point of the constrained problem. Preliminary numerical results demonstrate the efficiency of the penalty method for finding sparse solutions of underdetermined linear systems.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on optimization, 2016, v. 26, no. 3, p. 1465-1492en_US
dcterms.isPartOfSIAM journal on optimizationen_US
dcterms.issued2016-
dc.identifier.isiWOS:000386454800003-
dc.identifier.ros2016000247-
dc.identifier.eissn1095-7189en_US
dc.identifier.rosgroupid2016000246-
dc.description.ros2016-2017 > Academic research: refereed > Publication in refereed journalen_US
dc.description.validate201804_a bcmaen_US
dc.description.oaOther Versionen_US
dc.identifier.FolderNumberAMA-0565-
dc.description.fundingSourceSelf-fundeden_US
dc.description.pubStatusPublisheden_US
dc.identifier.OPUS6685164-
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