| dc.creator | Fawzi, Hamza | |
| dc.creator | Saunderson, J | |
| dc.date.accessioned | 2016-10-13 | |
| dc.date.accessioned | 2018-11-24T23:19:59Z | |
| dc.date.available | 2017-08-16T09:38:18Z | |
| dc.date.available | 2018-11-24T23:19:59Z | |
| dc.date.issued | 2017-01-15 | |
| dc.identifier | https://www.repository.cam.ac.uk/handle/1810/266464 | |
| dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3524 | |
| dc.description.abstract | A 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.language | en | |
| dc.publisher | Linear Algebra and Its Applications | |
| dc.title | Lieb's concavity theorem, matrix geometric means, and semidefinite optimization | |
| dc.type | Article | |
