An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications

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dc.contributor.author Dostál, Zdeněk
dc.contributor.author Kozubek, Tomáš
dc.date.accessioned 2012-11-07T13:05:15Z
dc.date.available 2012-11-07T13:05:15Z
dc.date.issued 2012
dc.identifier.citation Mathematical programming. 2012, vol. 135, no. 1-2, p. 195-220. cs
dc.identifier.issn 0025-5610
dc.identifier.issn 1436-4646
dc.identifier.uri http://hdl.handle.net/10084/95676
dc.description.abstract We 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.extent 749728 bytes cs
dc.format.mimetype application/pdf cs
dc.language.iso en cs
dc.publisher Springer cs
dc.relation.ispartofseries Mathematical programming cs
dc.relation.uri http://dx.doi.org/10.1007/s10107-011-0454-2 cs
dc.subject QPQC with separable constraints cs
dc.subject spherical constraints cs
dc.subject rate of convergence cs
dc.subject 65K10 cs
dc.subject 90C20 cs
dc.subject 90C25 cs
dc.subject 90C90 cs
dc.title An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications cs
dc.type article cs
dc.identifier.location Není ve fondu ÚK cs
dc.identifier.doi 10.1007/s10107-011-0454-2
dc.rights.access openAccess
dc.type.version submittedVersion
dc.type.status Peer-reviewed cs
dc.description.source Web of Science cs
dc.description.volume 135 cs
dc.description.issue 1-2 cs
dc.description.lastpage 220 cs
dc.description.firstpage 195 cs
dc.identifier.wos 000308647100007

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