Sufficient second-order optimality conditions for convex control constraints

dc.contributor.authorWachsmuth, Daniel
dc.date.accessioned2021-12-17T10:05:55Z
dc.date.available2021-12-17T10:05:55Z
dc.date.issued2004-10-18
dc.description.abstractIn this article sufficient optimality conditions are established for optimal control problems with pointwise convex control constraints. Here, the control is a function with values in Rn. The constraint is of the form u(x) āˆˆ U(x), where U is an set-valued mapping that is assumed to be measurable with convex and closed images. The second-order condition requires coercivity of the Lagrange function on a suitable subspace, which excludes strongly active constraints, together with first-order necessary conditions. It ensures local optimality of a reference function in a Lāˆž-neighborhood. The analysis is done for a model problem namely the optimal distributed control of the instationary Navier-Stokes equations.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15525
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14298
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otheroptimal controlen
dc.subject.othersufficient second-order conditionsen
dc.subject.otherstrongly active setsen
dc.subject.otherconvex control constraintsen
dc.subject.othermeasurable set-valued functionsen
dc.subject.otherNavier-Stokes equationsen
dc.titleSufficient second-order optimality conditions for convex control constraintsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische UniversitƤt Berlinen
tub.series.issuenumber2004, 30en
tub.series.namePreprint-Reihe des Instituts fĆ¼r Mathematik, Technische UniversitƤt Berlinen
tub.subject.msc200049K20 Problems involving partial differential equationsen
tub.subject.msc200026E25 Set-valued functionsen
tub.subject.msc200049J53 Set-valued and variational analysisen
tub.subject.msc200076D05 Navier-Stokes equationsen

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