Computation of Minimum Volume Covering Ellipsoids
Author(s)Sun, Peng; Freund, Robert M.
We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points al,...,am C Rn . This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30, 000 and n = 30) to a high degree of accuracy in under 30 seconds on a personal computer.
Massachusetts Institute of Technology, Operations Research Center
Operations Research Center Working Paper;OR 364-02
Ellipsoid, Newton's method, interior-point method, barrier method, active set, semidefinite program, data mining.