Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/76268
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorLiu, TXen_US
dc.creatorPong, TKen_US
dc.date.accessioned2018-05-10T02:55:40Z-
dc.date.available2018-05-10T02:55:40Z-
dc.identifier.issn0926-6003en_US
dc.identifier.urihttp://hdl.handle.net/10397/76268-
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rights© Springer Science+Business Media New York 2017en_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/s10589-017-9900-2en_US
dc.subjectForward-backward envelopeen_US
dc.subjectKurdyka-Lojasiewicz propertyen_US
dc.subjectDifference-of-convex programmingen_US
dc.titleFurther properties of the forward-backward envelope with applications to difference-of-convex programmingen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage489en_US
dc.identifier.epage520en_US
dc.identifier.volume67en_US
dc.identifier.issue3en_US
dc.identifier.doi10.1007/s10589-017-9900-2en_US
dcterms.abstractIn this paper, we further study the forward-backward envelope first introduced in Patrinos and Bemporad (Proceedings of the IEEE Conference on Decision and Control, pp 2358-2363, 2013) and Stella et al. (Comput Optim Appl, doi:10.1007/s10589-017-9912-y, 2017) for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the original problem for the corresponding forward-backward envelope to be a level-bounded and Kurdyka-Aojasiewicz function with an exponent of ; these results are important for the efficient minimization of the forward-backward envelope by classical optimization algorithms. In addition, we demonstrate how to minimize some difference-of-convex regularized least squares problems by minimizing a suitably constructed forward-backward envelope. Our preliminary numerical results on randomly generated instances of large-scale regularized least squares problems (Yin et al. in SIAM J Sci Comput 37:A536-A563, 2015) illustrate that an implementation of this approach with a limited-memory BFGS scheme usually outperforms standard first-order methods such as the nonmonotone proximal gradient method in Wright et al. (IEEE Trans Signal Process 57:2479-2493, 2009).en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationComputational optimization and applications, July 2017, v. 67, no. 3, p. 489-520en_US
dcterms.isPartOfComputational optimization and applicationsen_US
dcterms.issued2017-07-
dc.identifier.isiWOS:000401999900002-
dc.identifier.scopus2-s2.0-85012923479-
dc.identifier.eissn1573-2894en_US
dc.identifier.rosgroupid2017000099-
dc.description.ros2017-2018 > Academic research: refereed > Publication in refereed journalen_US
dc.description.validate201805 bcrcen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumbera0585-n01-
dc.identifier.SubFormID280-
dc.description.fundingSourceRGCen_US
dc.description.fundingText25300815en_US
dc.description.pubStatusPublisheden_US
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