Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/79655
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorWen, Ben_US
dc.creatorChen, XJen_US
dc.creatorPong, TKen_US
dc.date.accessioned2018-12-21T07:12:57Z-
dc.date.available2018-12-21T07:12:57Z-
dc.identifier.issn0926-6003en_US
dc.identifier.urihttp://hdl.handle.net/10397/79655-
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rights© Springer Science+Business Media, LLC 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/s10589-017-9954-1en_US
dc.subjectDifference-of-convex problemsen_US
dc.subjectNonconvexen_US
dc.subjectNonsmoothen_US
dc.subjectExtrapolationen_US
dc.subjectKurdyka-Lojasiewicz inequalityen_US
dc.titleA proximal difference-of-convex algorithm with extrapolationen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage297en_US
dc.identifier.epage324en_US
dc.identifier.volume69en_US
dc.identifier.issue2en_US
dc.identifier.doi10.1007/s10589-017-9954-1en_US
dcterms.abstractWe consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical difference-of-convex algorithm (DCA) (Pham et al. Acta Math Vietnam 22:289-355, 1997), the difficulty of the subproblems of this algorithm depends heavily on the choice of DC decomposition. Simpler subproblems can be obtained by using a specific DC decomposition described in Pham et al. (SIAM J Optim 8:476-505, 1998). This decomposition has been proposed in numerous work such as Gotoh et al. (DC formulations and algorithms for sparse optimization problems, 2017), and we refer to the resulting DCA as the proximal DCA. Although the subproblems are simpler, the proximal DCA is the same as the proximal gradient algorithm when the concave part of the objective is void, and hence is potentially slow in practice. In this paper, motivated by the extrapolation techniques for accelerating the proximal gradient algorithm in the convex settings, we consider a proximal difference-of-convex algorithm with extrapolation to possibly accelerate the proximal DCA. We show that any cluster point of the sequence generated by our algorithm is a stationary point of the DC optimization problem for a fairly general choice of extrapolation parameters: in particular, the parameters can be chosen as in FISTA with fixed restart (O'Donoghue and CandSs in Found Comput Math 15, 715-732, 2015). In addition, by assuming the Kurdyka-Aojasiewicz property of the objective and the differentiability of the concave part, we establish global convergence of the sequence generated by our algorithm and analyze its convergence rate. Our numerical experiments on two difference-of-convex regularized least squares models show that our algorithm usually outperforms the proximal DCA and the general iterative shrinkage and thresholding algorithm proposed in Gong et al. (A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems, 2013).en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationComputational optimization and applications, Mar. 2018, v. 69, no. 2, p. 297-324en_US
dcterms.isPartOfComputational optimization and applicationsen_US
dcterms.issued2018-03-
dc.identifier.isiWOS:000426295000002-
dc.identifier.eissn1573-2894en_US
dc.identifier.rosgroupid2017000102-
dc.description.ros2017-2018 > Academic research: refereed > Publication in refereed journalen_US
dc.description.validate201812 bcrcen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumbera0585-n03-
dc.identifier.SubFormID282-
dc.description.fundingSourceRGCen_US
dc.description.fundingText25300815en_US
dc.description.pubStatusPublisheden_US
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