Computation of Minimum-Volume Covering Ellipsoids

Peng Sun () and Robert M. Freund ()
Additional contact information
Peng Sun: The Fuqua School of Business, Duke University, Box 90120, Durham, North Carolina 27708
Robert M. Freund: Sloan School of Management, Massachusetts Institute of Technology, 50 Memorial Drive, Cambridge, Massachusetts 02142

Operations Research, 2004, vol. 52, issue 5, 690-706

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 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (9)

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