Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/90721
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorYe, Men_US
dc.creatorPong, TKen_US
dc.date.accessioned2021-08-31T01:04:50Z-
dc.date.available2021-08-31T01:04:50Z-
dc.identifier.issn1052-6234en_US
dc.identifier.urihttp://hdl.handle.net/10397/90721-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2020 Society for Industrial and Applied Mathematicsen_US
dc.rightsFirst Published in SIAM Journal on Optimization in Volume 30, Issue 2, published by the Society for Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.en_US
dc.subjectKurdyka-Łojasiewicz propertyen_US
dc.subjectMaximum feasible subsystemen_US
dc.subjectSubgradient methodsen_US
dc.titleA subgradient-based approach for finding the maximum feasible subsystem with respect to a seten_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage1274en_US
dc.identifier.epage1299en_US
dc.identifier.volume30en_US
dc.identifier.issue2en_US
dc.identifier.doi10.1137/18M1186320en_US
dcterms.abstractWe propose a subgradient-based method for finding the maximum feasible subsystem in a collection of closed sets with respect to a given closed set C (MFSC). In this method, we reformulate the MFSC problem as an ℓ0 optimization problem and construct a sequence of continuous optimization problems to approximate it. The objective of each approximation problem is the sum of the composition of a nonnegative nondecreasing continuously differentiable concave function with the squared distance function to a closed set. Although this objective function is nonsmooth in general, a subgradient can be obtained in terms of the projections onto the closed sets. Based on this observation, we adapt a subgradient projection method to solve these approximation problems. Unlike classical subgradient methods, the convergence (clustering to stationary points) of our subgradient method is guaranteed with a nondiminishing stepsize under mild assumptions. This allows us to further study the sequential convergence of the subgradient method under suitable Kurdyka-Łojasiewicz assumptions. Finally, we illustrate our algorithm numerically for solving the MFSC problems on a collection of halfspaces and a collection of unions of halfspaces, respectively, with respect to the set of s-sparse vectors.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on optimization, 2020, v. 30, no. 2, p. 1274-1299en_US
dcterms.isPartOfSIAM journal on optimizationen_US
dcterms.issued2020-
dc.identifier.scopus2-s2.0-85085253861-
dc.identifier.eissn1095-7189en_US
dc.description.validate202108 bchyen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumbera1017-n02-
dc.identifier.SubFormID2438-
dc.description.fundingSourceRGCen_US
dc.description.fundingTextPolyU153005/17pen_US
dc.description.pubStatusPublisheden_US
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