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dc.contributor.authorDostál, Zdeněk
dc.contributor.authorKozubek, Tomáš
dc.date.accessioned2012-11-07T13:05:15Z
dc.date.available2012-11-07T13:05:15Z
dc.date.issued2012
dc.identifier.citationMathematical programming. 2012, vol. 135, no. 1-2, p. 195-220.cs
dc.identifier.issn0025-5610
dc.identifier.issn1436-4646
dc.identifier.urihttp://hdl.handle.net/10084/95676
dc.description.abstractWe propose a modification of our MPGP algorithm for the solution of bound constrained quadratic programming problems so that it can be used for minimization of a strictly convex quadratic function subject to separable convex constraints. Our active set based algorithm explores the faces by conjugate gradients and changes the active sets and active variables by gradient projections, possibly with the superrelaxation steplength. The error estimate in terms of extreme eigenvalues guarantees that if a class of minimization problems has the spectrum of the Hessian matrix in a given positive interval, then the algorithm can find and recognize an approximate solution of any particular problem in a number of iterations that is uniformly bounded. We also show how to use the algorithm for the solution of separable and equality constraints. The power of our algorithm and its optimality are demonstrated on the solution of a problem of two cantilever beams in mutual contact with Tresca friction discretized by almost twelve millions nodal variables.cs
dc.format.extent749728 bytescs
dc.format.mimetypeapplication/pdfcs
dc.language.isoencs
dc.publisherSpringercs
dc.relation.ispartofseriesMathematical programmingcs
dc.relation.urihttp://dx.doi.org/10.1007/s10107-011-0454-2cs
dc.subjectQPQC with separable constraintscs
dc.subjectspherical constraintscs
dc.subjectrate of convergencecs
dc.subject65K10cs
dc.subject90C20cs
dc.subject90C25cs
dc.subject90C90cs
dc.titleAn optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applicationscs
dc.typearticlecs
dc.identifier.locationNení ve fondu ÚKcs
dc.identifier.doi10.1007/s10107-011-0454-2
dc.rights.accessopenAccess
dc.type.versionsubmittedVersion
dc.type.statusPeer-reviewedcs
dc.description.sourceWeb of Sciencecs
dc.description.volume135cs
dc.description.issue1-2cs
dc.description.lastpage220cs
dc.description.firstpage195cs
dc.identifier.wos000308647100007


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