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Special Seminar in Computing and Mathematical Sciences

Monday, November 5, 2018
1:30pm to 2:30pm
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Annenberg 105
Semidefinite Approximations of the Matrix Logarithm (and related functions)
Pablo Parrilo, Massachusetts Institute of Technology,

We propose a new way to treat the exponential/relative entropy cone using symmetric cone solvers. Our approach is based on a combination of highly accurate rational (Padé) approximations and a functional equation. A key property of this technique is that these rational approximations, by construction, inherit the (operator) concavity of the logarithm. As a consequence, our method extends to the matrix logarithm and other derived functions such as the matrix relative entropy, giving new semidefinite optimization-based tools for convex optimization involving these functions. We include an implementation of our method for the MATLAB-based parser CVX. We compare our method to existing approximation schemes, and show that it can be much faster, especially for large problems. Preprint at Joint work with Hamza Fawzi (Cambridge) and James Saunderson (Monash).

For more information, please contact Diana Bohler by phone at x1768 or by email at [email protected].