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CATEGORIES:CUED Control Group Seminars
SUMMARY:Semidefinite approximations of matrix logarithm -
Hamza Fawzi\, University of Cambridge
DTSTART;TZID=Europe/London:20161103T140000
DTEND;TZID=Europe/London:20161103T150000
UID:TALK68866AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68866
DESCRIPTION:The matrix logarithm\, when applied to symmetric p
ositive definite matrices satisfies a notable conc
avity property in the positive semidefinite (Loewn
er) order. This concavity property is a cornerston
e result in the study of operator convex functions
and has important applications in matrix concentr
ation inequalities and quantum information theory.
\nIn this talk I will show that certain rational a
pproximations of the matrix logarithm remarkably p
reserve this concavity property and moreover\, are
amenable to semidefinite programming. Such approx
imations allow us to use off-the-shelf semidefinit
e programming solvers for convex optimization prob
lems involving the matrix logarithm. These approxi
mations are also useful in the scalar case and pro
vide a much faster alternative to existing methods
based on successive approximation for problems in
volving the exponential/relative entropy cone. I w
ill conclude by showing some applications to probl
ems arising in quantum information theory.\n\nThis
is joint work with James Saunderson (Monash Unive
rsity) and Pablo Parrilo (MIT)
LOCATION: Cambridge University Engineering Department\, JDB
Seminar Room
CONTACT:Tim Hughes
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