Computation of Minimum-Volume Covering Ellipsoids
Operations Research · 2004 · Volume 52 · Issue 5
Abstract
We present a practical algorithm for computing the minimum-volume n -dimensional ellipsoid that must contain m given points a 1 ,…, a m ∈ ℝ n . 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.
Keywords
programming, nonlinear, algorithms, large-scale systems, statistics, cluster analysis, data analysis, mathematics, convexity, matrices
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