BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Semidefinite approximations of matrix logarithm - Hamza Fawzi\, Un
 iversity of Cambridge
DTSTART:20161103T140000Z
DTEND:20161103T150000Z
UID:TALK68866@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:The matrix logarithm\, when applied to symmetric positive defi
 nite matrices satisfies a notable concavity property in the positive semid
 efinite (Loewner) order. This concavity property is a cornerstone result i
 n the study of operator convex functions and has important applications in
  matrix concentration inequalities and quantum information theory.\nIn thi
 s talk I will show that certain rational approximations of the matrix loga
 rithm remarkably preserve this concavity property and moreover\, are amena
 ble to semidefinite programming. Such approximations allow us to use off-t
 he-shelf semidefinite programming solvers for convex optimization problems
  involving the matrix logarithm. These approximations are also useful in t
 he scalar case and provide a much faster alternative to existing methods b
 ased on successive approximation for problems involving the exponential/re
 lative entropy cone. I will conclude by showing some applications to probl
 ems arising in quantum information theory.\n\nThis is joint work with Jame
 s Saunderson (Monash University) and Pablo Parrilo (MIT)
LOCATION: Cambridge University Engineering Department\, JDB Seminar Room
END:VEVENT
END:VCALENDAR