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dc.contributor.authorFawzi, Hamzaen
dc.contributor.authorSaunderson, Jen
dc.date.accessioned2017-08-16T09:38:18Z
dc.date.available2017-08-16T09:38:18Z
dc.date.issued2017-01-15en
dc.identifier.issn0024-3795
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/266464
dc.description.abstractA famous result of Lieb establishes that the map (A,B)↦tr[K^* A^{1−t}KB^{t}] is jointly concave in the pair (A,B) of positive definite matrices, where K is a fixed matrix and t∈[0,1]. In this paper we show that Lieb's function admits an explicit semidefinite programming formulation for any rational t∈[0,1]. Our construction makes use of a semidefinite formulation of weighted matrix geometric means. We provide an implementation of our constructions in Matlab.
dc.description.sponsorshipHamza Fawzi was supported in part by AFOSR FA9550-11-1-0305. James Saunderson was supported by NSF grant CCF-1409836.
dc.language.isoenen
dc.publisherElsevier
dc.subjectMatrix convexityen
dc.subjectSemidefinite optimizationen
dc.subjectLinear matrix inequalitiesen
dc.subjectLieb's concavity theoremen
dc.subjectMatrix geometric meansen
dc.titleLieb's concavity theorem, matrix geometric means, and semidefinite optimizationen
dc.typeArticle
prism.endingPage263
prism.publicationDate2017en
prism.publicationNameLinear Algebra and Its Applicationsen
prism.startingPage240
prism.volume513en
dc.identifier.doi10.17863/CAM.9714
dcterms.dateAccepted2016-10-13en
rioxxterms.versionofrecord10.1016/j.laa.2016.10.012en
rioxxterms.versionAMen
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
rioxxterms.licenseref.startdate2017-01-15en
dc.contributor.orcidFawzi, Hamza [0000-0001-6026-4102]
dc.identifier.eissn1873-1856
rioxxterms.typeJournal Article/Reviewen
cam.issuedOnline2016-10-17en
dc.identifier.urlhttps://www.sciencedirect.com/science/article/pii/S0024379516304852?via%3Dihub#!en
rioxxterms.freetoread.startdate2018-08-24


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