Semidefinite approximations of matrix logarithm

Add to your list(s) Download to your calendar using vCal

• Hamza Fawzi, University of Cambridge
• Thursday 03 November 2016, 14:00-15:00
• Cambridge University Engineering Department, JDB Seminar Room.

If you have a question about this talk, please contact Tim Hughes.

The matrix logarithm, when applied to symmetric positive definite matrices satisfies a notable concavity property in the positive semidefinite (Loewner) order. This concavity property is a cornerstone result in the study of operator convex functions and has important applications in matrix concentration inequalities and quantum information theory. In this talk I will show that certain rational approximations of the matrix logarithm remarkably preserve this concavity property and moreover, are amenable to semidefinite programming. Such approximations allow us to use off-the-shelf semidefinite programming solvers for convex optimization problems involving the matrix logarithm. These approximations are also useful in the scalar case and provide a much faster alternative to existing methods based on successive approximation for problems involving the exponential/relative entropy cone. I will conclude by showing some applications to problems arising in quantum information theory.

This is joint work with James Saunderson (Monash University) and Pablo Parrilo (MIT)

This talk is part of the CUED Control Group Seminars series.

This talk is included in these lists:

• Cambridge University Engineering Department, JDB Seminar Room
• All CMS events
• All Talks (aka the CURE list)
• CCIMI
• CCIMI Seminars
• CMS Events
• CUED Control Group Seminars
• Cambridge Centre for Data-Driven Discovery (C2D3)
• Cambridge University Engineering Department Talks
• Cambridge talks
• Centre for Smart Infrastructure & Construction
• Chris Davis' list
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Featured lists
• Guy Emerson's list
• Hanchen DaDaDash
• Information Engineering Division seminar list
• Interested Talks
• School of Physical Sciences
• School of Technology
• Signal Processing and Communications Lab Seminars
• Statistical Laboratory info aggregator
• Trust & Technology Initiative - interesting events
• bld31
• custom
• ndk22's list
• ob366-ai4er
• rp587

Note that ex-directory lists are not shown.