Special Seminar in Computing and Mathematical Sciences
Pablo A. Parrilo is the Joseph F. and Nancy P. Keithley Professor of Electrical Engineering and Computer Science at MIT, with a joint appointment in Mathematics. He is affiliated with the Laboratory for Information and Decision Systems (LIDS) and the Operations Research Center (ORC). Past appointments include Assistant Professor at the Automatic Control Laboratory of the Swiss Federal Institute of Technology (ETH Zurich), and Visiting Associate Professor at the California Institute of Technology. He received an Electronics Engineering undergraduate degree from the University of Buenos Aires, and a PhD in Control and Dynamical Systems from the California Institute of Technology. His research interests include mathematical optimization, machine learning, control and identification, robustness analysis and synthesis, and the development and application of computational tools based on convex optimization and algorithmic algebra to practically relevant engineering problems. Prof. Parrilo has received several distinctions, including the Donald P. Eckman Award of the American Automatic Control Council, the SIAM Activity Group on Control and Systems Theory (SIAG/CST) Prize, the IEEE Antonio Ruberti Young Researcher Prize, and the Farkas Prize of the INFORMS Optimization Society. He is an IEEE and SIAM Fellow.
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).