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Article: A Peaceman–Rachford Splitting Method with Monotone Plus Skew-Symmetric Splitting for Nonlinear Saddle Point Problems

TitleA Peaceman–Rachford Splitting Method with Monotone Plus Skew-Symmetric Splitting for Nonlinear Saddle Point Problems
Authors
KeywordsSaddle point problem
Peaceman–Rachford splitting method
Hermitian and skew-Hermitian splitting method
Contraction
Issue Date2019
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0885-7474
Citation
Journal of Scientific Computing, 2019, v. 81 n. 2, p. 763-788 How to Cite?
AbstractThis paper is devoted to solving the linearly constrained convex optimization problems by Peaceman–Rachford splitting method with monotone plus skew-symmetric splitting on KKT operators. This approach generalizes the Hermitian and skew-Hermitian splitting method, an unconditionally convergent algorithm for non-Hermitian positive definite linear systems, to the nonlinear scenario. The convergence of the proposed algorithm is guaranteed under some mild assumptions, e.g., the strict convexity on objective functions and the consistency on constraints, even though the Lions–Mercier property is not fulfilled. In addition, we explore an inexact version of the proposed algorithm, which allows solving the subproblems approximately with some inexactness criteria. Numerical simulations on an image restoration problem demonstrate the compelling performance of the proposed algorithm.
Persistent Identifierhttp://hdl.handle.net/10722/288101
ISSN
2019 Impact Factor: 2.228
2015 SCImago Journal Rankings: 1.724
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorDing, W-
dc.contributor.authorNg, MK-
dc.contributor.authorZhang, W-
dc.date.accessioned2020-10-05T12:07:53Z-
dc.date.available2020-10-05T12:07:53Z-
dc.date.issued2019-
dc.identifier.citationJournal of Scientific Computing, 2019, v. 81 n. 2, p. 763-788-
dc.identifier.issn0885-7474-
dc.identifier.urihttp://hdl.handle.net/10722/288101-
dc.description.abstractThis paper is devoted to solving the linearly constrained convex optimization problems by Peaceman–Rachford splitting method with monotone plus skew-symmetric splitting on KKT operators. This approach generalizes the Hermitian and skew-Hermitian splitting method, an unconditionally convergent algorithm for non-Hermitian positive definite linear systems, to the nonlinear scenario. The convergence of the proposed algorithm is guaranteed under some mild assumptions, e.g., the strict convexity on objective functions and the consistency on constraints, even though the Lions–Mercier property is not fulfilled. In addition, we explore an inexact version of the proposed algorithm, which allows solving the subproblems approximately with some inexactness criteria. Numerical simulations on an image restoration problem demonstrate the compelling performance of the proposed algorithm.-
dc.languageeng-
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0885-7474-
dc.relation.ispartofJournal of Scientific Computing-
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: https://doi.org/[insert DOI]-
dc.subjectSaddle point problem-
dc.subjectPeaceman–Rachford splitting method-
dc.subjectHermitian and skew-Hermitian splitting method-
dc.subjectContraction-
dc.titleA Peaceman–Rachford Splitting Method with Monotone Plus Skew-Symmetric Splitting for Nonlinear Saddle Point Problems-
dc.typeArticle-
dc.identifier.emailNg, MK: michael.ng@hku.hk-
dc.identifier.authorityNg, MK=rp02578-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10915-019-01034-w-
dc.identifier.scopuseid_2-s2.0-85073623953-
dc.identifier.hkuros315740-
dc.identifier.volume81-
dc.identifier.issue2-
dc.identifier.spage763-
dc.identifier.epage788-
dc.identifier.isiWOS:000491440200006-
dc.publisher.placeUnited States-
dc.identifier.issnl0885-7474-

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