Computation of Minimum-Volume Covering Ellipsoids

We present a practical algorithm for computing the minimum-volume n-dimensional ellipsoid that must contain m given points a₁,…,a_m ∈ 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.