Computation of Minimum Volume Covering Ellipsoids

Peng Sun (psunmit.edu)
Robert M. Freund (rfreundmit.edu)

Abstract: We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a_1, …, a_m \in 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: Ellipsoid, Newton's method, interior-point method, barrier method, active set, semidefinite program, data mining

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Applications -- OR and Management Sciences

Citation: MIT Operations Research Center Working Paper OR 064-02

Download: [Postscript]

Entry Submitted: 07/31/2002
Entry Accepted: 07/31/2002
Entry Last Modified: 07/31/2002

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