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dc.contributor.authorWolfmayr, Monika
dc.date.accessioned2020-06-29T11:12:52Z
dc.date.available2020-06-29T11:12:52Z
dc.date.issued2020
dc.identifier.citationWolfmayr, M. (2020). Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems. <i>Computers and mathematics with applications</i>, <i>80</i>(5), 1050-1072. <a href="https://doi.org/10.1016/j.camwa.2020.04.021" target="_blank">https://doi.org/10.1016/j.camwa.2020.04.021</a>
dc.identifier.otherCONVID_35989427
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/70974
dc.description.abstractIn this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to large systems of linear equations having a saddle point structure. The derivation of preconditioners for the minimal residual method for the new optimization problem is discussed in more detail. Finally, several numerical experiments for both optimal control problems are presented confirming the theoretical results obtained. This work provides the basis for an adaptive scheme for time-periodic optimization problems.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofseriesComputers and mathematics with applications
dc.rightsCC BY-NC-ND 4.0
dc.subject.othera posteriori error analysis
dc.subject.otherparabolic optimal control problems
dc.subject.othertime-periodic condition
dc.subject.othermultiharmonic finite element method
dc.subject.othertwo-sided bounds
dc.subject.otherguaranteed lower bounds
dc.titleGuaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202006295160
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1050-1072
dc.relation.issn0898-1221
dc.relation.numberinseries5
dc.relation.volume80
dc.type.versionacceptedVersion
dc.rights.copyright© 2020 Elsevier Ltd.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber295897
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysonumeerinen analyysi
dc.subject.ysomatemaattinen optimointi
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p15833
jyx.subject.urihttp://www.yso.fi/onto/yso/p17635
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1016/j.camwa.2020.04.021
dc.relation.funderSuomen Akatemiafi
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundinginformationThe author gratefully acknowledges the financial support by the Academy of Finland under the grant 295897 and by the Central Finland regional Fund of the Finnish Cultural Foundation


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