Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/90720
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorLiu, Ten_US
dc.creatorPong, TKen_US
dc.creatorTakeda, Aen_US
dc.date.accessioned2021-08-31T01:04:49Z-
dc.date.available2021-08-31T01:04:49Z-
dc.identifier.issn0926-6003en_US
dc.identifier.urihttp://hdl.handle.net/10397/90720-
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rights© Springer Science+Business Media, LLC, part of Springer Nature 2019en_US
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in Computational Optimization and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10589-019-00067-z.en_US
dc.subjectDifference-of-convex optimizationen_US
dc.subjectKurdyka–Lojasiewicz propertyen_US
dc.subjectOutlier detectionen_US
dc.subjectSparse recoveryen_US
dc.titleA refined convergence analysis of pDCAe with applications to simultaneous sparse recovery and outlier detectionen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage69en_US
dc.identifier.epage100en_US
dc.identifier.volume73en_US
dc.identifier.issue1en_US
dc.identifier.doi10.1007/s10589-019-00067-zen_US
dcterms.abstractWe consider the problem of minimizing a difference-of-convex (DC) function, which can be written as the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous possibly nonsmooth concave function. We refine the convergence analysis in Wen et al. (Comput Optim Appl 69, 297–324, 2018) for the proximal DC algorithm with extrapolation (pDCA e ) and show that the whole sequence generated by the algorithm is convergent without imposing differentiability assumptions in the concave part. Our analysis is based on a new potential function and we assume such a function is a Kurdyka–Łojasiewicz (KL) function. We also establish a relationship between our KL assumption and the one used in Wen et al. (2018). Finally, we demonstrate how the pDCA e can be applied to a class of simultaneous sparse recovery and outlier detection problems arising from robust compressed sensing in signal processing and least trimmed squares regression in statistics. Specifically, we show that the objectives of these problems can be written as level-bounded DC functions whose concave parts are typically nonsmooth. Moreover, for a large class of loss functions and regularizers, the KL exponent of the corresponding potential function are shown to be 1/2, which implies that the pDCA e is locally linearly convergent when applied to these problems. Our numerical experiments show that the pDCA e usually outperforms the proximal DC algorithm with nonmonotone linesearch (Liu et al. in Math Program, 2018. https://doi.org/10.1007/s10107-018-1327-8, Appendix A) in both CPU time and solution quality for this particular application.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationComputational optimization and applications, 15 May 2019, v. 73, no. 1, p. 69-100en_US
dcterms.isPartOfComputational optimization and applicationsen_US
dcterms.issued2019-05-15-
dc.identifier.scopus2-s2.0-85060692443-
dc.identifier.eissn1573-2894en_US
dc.description.validate202108 bchyen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumbera1017-n01-
dc.identifier.SubFormID2437-
dc.description.fundingSourceRGCen_US
dc.description.fundingTextPolyU153005/17pen_US
dc.description.pubStatusPublisheden_US
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