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Optimization schemes on manifolds for structured matrices with fixed eigenvalues

2024-12-02Artigo científico Acesso aberto
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dc.contributor.authorChehab, Jean Paul
dc.contributor.authorOviedo, Harry
dc.contributor.authorRaydan, Marcos
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.pblSpringer Science Business Media
dc.date.accessioned2025-02-14T21:23:03Z
dc.date.available2025-02-14T21:23:03Z
dc.date.issued2024-12-02
dc.descriptionFunding Information: Open access funding provided by FCT|FCCN (b-on). The second author was financially supported by the Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Chile, through the FES startup package for scientific research. The third author was financially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) under the scope of projects UIDB/MAT/00297/2020 (doi.org/10.54499/UIDB/00297/2020) and UIDP/MAT/00297/2020 (doi.org/10.54499/UIDP/00297/2020) (Centro de Matemática e Aplicações). Publisher Copyright: © The Author(s) 2024.
dc.description.abstractSeveral manifold optimization schemes are presented and analyzed for solving a specialized inverse structured symmetric matrix problem with prescribed spectrum. Some entries in the desired matrix are assigned in advance and cannot be altered. The rest of the entries are free, some of them preferably away from zero. The reconstructed matrix must satisfy these requirements and its eigenvalues must be the given ones. This inverse eigenvalue problem is related to the problem of determining the graph, with weights on the undirected edges, of the matrix associated with its sparse pattern. Our optimization schemes are based on considering the eigenvector matrix as the only unknown and iteratively moving on the manifold of orthogonal matrices, forcing the additional structural requirements through a change of variables and a convenient differentiable objective function in the space of square matrices. We propose Riemannian gradient-type methods combined with two different well-known retractions, and with two well-known constrained optimization strategies: penalization and augmented Lagrangian. We also present a block alternating technique that takes advantage of a proper separation of variables. Convergence properties of the penalty alternating approach are established. Finally, we present initial numerical results to demonstrate the effectiveness of our proposals.en
dc.description.versionpublishersversion
dc.description.versioninpress
dc.format.extent26
dc.format.extent502513
dc.identifier.doi10.1007/s10589-024-00630-3
dc.identifier.issn0926-6003
dc.identifier.otherPURE: 110436314
dc.identifier.otherPURE UUID: 65f74afd-4ec9-4903-ab0c-8c073036f7ac
dc.identifier.otherScopus: 85198153403
dc.identifier.otherWOS: 001375587400001
dc.identifier.urihttp://hdl.handle.net/10362/179085
dc.identifier.urlhttps://www.scopus.com/pages/publications/85198153403
dc.language.isoeng
dc.peerreviewedyes
dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT
dc.relationCenter for Mathematics and Applications
dc.relationCenter for Mathematics and Applications
dc.subjectAlternating direction method of multipliers
dc.subjectAugmented Lagrangian
dc.subjectInverse eigenvalue problems
dc.subjectRiemannian optimization
dc.subjectSpectral graph theory
dc.subjectStiefel manifold
dc.subjectControl and Optimization
dc.subjectComputational Mathematics
dc.subjectApplied Mathematics
dc.titleOptimization schemes on manifolds for structured matrices with fixed eigenvaluesen
dc.typejournal article
degois.publication.firstPage1
degois.publication.issue1
degois.publication.lastPage26
degois.publication.titleComputational Optimization And Applications
degois.publication.volume90
dspace.entity.typePublication
oaire.awardNumberUIDB/00297/2020
oaire.awardNumberUIDP/00297/2020
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublicationd00ae22f-ec2b-47b2-935e-60cb44493cc6
relation.isProjectOfPublication65d392f7-8781-4d70-b9f3-069b07d4a311
relation.isProjectOfPublication.latestForDiscovery65d392f7-8781-4d70-b9f3-069b07d4a311

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