Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/89219
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorChen, Cen_US
dc.creatorPong, TKen_US
dc.creatorTan, Len_US
dc.creatorZeng, Len_US
dc.date.accessioned2021-02-18T09:15:27Z-
dc.date.available2021-02-18T09:15:27Z-
dc.identifier.issn0925-5001en_US
dc.identifier.urihttp://hdl.handle.net/10397/89219-
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rights© Springer Science+Business Media, LLC, part of Springer Nature 2020en_US
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in Journal of Global Optimization. The final authenticated version is available online at: https://dx.doi.org/10.1007/s10898-020-00899-8.en_US
dc.subjectDifference-of-convex optimizationen_US
dc.subjectMatrix factorizationsen_US
dc.subjectSplit feasibility problemsen_US
dc.titleA difference-of-convex approach for split feasibility with applications to matrix factorizations and outlier detectionen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage107en_US
dc.identifier.epage136en_US
dc.identifier.volume78en_US
dc.identifier.issue1en_US
dc.identifier.doi10.1007/s10898-020-00899-8en_US
dcterms.abstractThe split feasibility problem is to find an element in the intersection of a closed set C and the linear preimage of another closed set D, assuming the projections onto C and D are easy to compute. This class of problems arises naturally in many contemporary applications such as compressed sensing. While the sets C and D are typically assumed to be convex in the literature, in this paper, we allow both sets to be possibly nonconvex. We observe that, in this setting, the split feasibility problem can be formulated as an optimization problem with a difference-of-convex objective so that standard majorization-minimization type algorithms can be applied. Here we focus on the nonmonotone proximal gradient algorithm with majorization studied in Liu et al. (Math Program, 2019. https://doi.org/10.1007/s10107-018-1327-8, Appendix A). We show that, when this algorithm is applied to a split feasibility problem, the sequence generated clusters at a stationary point of the problem under mild assumptions. We also study local convergence property of the sequence under suitable assumptions on the closed sets involved. Finally, we perform numerical experiments to illustrate the efficiency of our approach on solving split feasibility problems that arise in completely positive matrix factorization, (uniformly) sparse matrix factorization, and outlier detection.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationJournal of global optimization, Sept. 2020, v. 78, no. 1, p. 107-136en_US
dcterms.isPartOfJournal of global optimizationen_US
dcterms.issued2020-09-
dc.identifier.scopus2-s2.0-85081923194-
dc.identifier.eissn1573-2916en_US
dc.description.rosembargo20211001en_US
dc.description.validate202102 bcwhen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumbera0585-n08-
dc.identifier.SubFormID287-
dc.description.fundingSourceRGCen_US
dc.description.fundingText15308516en_US
dc.description.pubStatusPublisheden_US
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