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Lieb's concavity theorem, matrix geometric means, and semidefinite optimization

dc.creatorFawzi, Hamza
dc.creatorSaunderson, J
dc.date.accessioned2016-10-13
dc.date.accessioned2018-11-24T23:19:59Z
dc.date.available2017-08-16T09:38:18Z
dc.date.available2018-11-24T23:19:59Z
dc.date.issued2017-01-15
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/266464
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3524
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.languageen
dc.publisherLinear Algebra and Its Applications
dc.titleLieb's concavity theorem, matrix geometric means, and semidefinite optimization
dc.typeArticle


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