Abstract
We discuss the convergence properties of first-order methods for two problems that arise in computational geometry and statistics: the minimum-volume enclosing ellipsoid problem and the minimum-area enclosing ellipsoidal cylinder problem for a set of m points in R^n. The algorithms are old but the analysis is new, and the methods are remarkably effective at solving large-scale problems to high accuracy.

Bio
Dr. Mike J. Todd is well-known for his contributions to linear and nonlinear optimization and game theory. His research interests are in algorithms for linear and convex programming, particularly semidefinite programming. He is interested in developing and analyzing interior-point methods; previous research interests include homotopy methods, probabilistic analysis of pivoting methods, and extensions of complementary pivoting ideas to oriented matroids.

Among his several awards, he has received the George B. Dantzig Prize jointly from the Mathematical Programming Society and SIAM in 1988, and the John von Neumann Theory Prize from INFORMS in 2003.