Special Seminar in Computing and Mathematical Sciences
Semidefinite Approximations of the Matrix Logarithm (and related functions)
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 https://arxiv.org/abs/1705.00812. Joint work with Hamza Fawzi (Cambridge) and James Saunderson (Monash).
Contact: Diana Bohler at x1768 email@example.com