Publication:
A subspace method for large-scale eigenvalue optimization

dc.contributor.coauthorMeerbergen, Karl
dc.contributor.coauthorMichiels, Wim
dc.contributor.departmentDepartment of Mathematics
dc.contributor.departmentGraduate School of Sciences and Engineering
dc.contributor.kuauthorKangal, Fatih
dc.contributor.kuauthorMengi, Emre
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.contributor.schoolcollegeinstituteGRADUATE SCHOOL OF SCIENCES AND ENGINEERING
dc.date.accessioned2024-11-09T13:14:29Z
dc.date.issued2018
dc.description.abstractWe consider the minimization or maximization of the Jth largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi, Yildirim, and Kilic [SIAM T. Matrix Anal. Appl., 35, pp. 699-724, 2014]. This work addresses the setting when the matrix-valued function involved is very large. We describe subspace procedures that convert the original problem into a small-scale one by means of orthogonal projections and restrictions to certain subspaces, and that gradually expand these subspaces based on the optimal solutions of small-scale problems. Global convergence and superlinear rate-of-convergence results with respect to the dimensions of the subspaces are presented in the infinite dimensional setting, where the matrix-valued function is replaced by a compact operator depending on parameters. In practice, it suffices to solve eigenvalue optimization problems involving matrices with sizes on the scale of tens, instead of the original problem involving matrices with sizes on the scale of thousands.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue1
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuEU - TÜBİTAK
dc.description.sponsorshipOPTEC
dc.description.sponsorshipOptimization in Engineering Center of KU Leuven
dc.description.sponsorshipResearch Foundation Flanders
dc.description.sponsorshipproject UCoCoS
dc.description.sponsorshipEuropean Union
dc.description.sponsorshipEuropean Commision
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TÜBİTAK) - FWO (Scientific and Technological Research Council of Turkey (TÜBİTAK) - Belgian Research Foundation, Flanders)
dc.description.sponsorshipBAGEP program of The Science Academy of Turkey
dc.description.versionPublisher version
dc.description.volume39
dc.identifier.doi10.1137/16M1070025
dc.identifier.eissn1095-7162
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR01492
dc.identifier.issn0895-4798
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-85045741528
dc.identifier.urihttps://doi.org/10.1137/16M1070025
dc.identifier.wos428949900003
dc.keywordsEigenvalue optimization
dc.keywordsLarge scale
dc.keywordsOrthogonal projection
dc.keywordsEigenvalue perturbation theory
dc.keywordsParameter dependent compact operator
dc.keywordsMatrix-valued function
dc.language.isoeng
dc.publisherSociety for Industrial and Applied Mathematics (SIAM)
dc.relation.grantnoG.0712.11N
dc.relation.grantno675080
dc.relation.grantnoPIRG-GA-268355
dc.relation.grantno113T053
dc.relation.ispartofSIAM Journal on Matrix Analysis and Applications
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/8060
dc.subjectMathematics, applied
dc.titleA subspace method for large-scale eigenvalue optimization
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorKangal, Fatih
local.contributor.kuauthorMengi, Emre
local.publication.orgunit1College of Sciences
local.publication.orgunit1GRADUATE SCHOOL OF SCIENCES AND ENGINEERING
local.publication.orgunit2Department of Mathematics
local.publication.orgunit2Graduate School of Sciences and Engineering
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