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Duality of ellipsoidal approximations via semi-infinite programming

Filiz Gurtuna (gurtuna1***at***math.umbc.edu)

Abstract: In this work, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi--infinite programming. We establish the known duality relationship between the minimum volume circumscribed ellipsoid problem and the optimal experimental design problem in statistics. The duality results are obtained using convex duality for semi--infinite programming developed in a functional analysis setting.

Keywords: Inscribed ellipsoid, circumscribed ellipsoid, minimum volume, maximum volume, duality, semi--infinite programming, optimality conditions, optimal experimental design, D-optimal design, John ellipsoid, Lowner ellipsoid

Category 1: Infinite Dimensional Optimization (Semi-infinite Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Technical Report TR2008-3, Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA, February/2008

Download: [PDF]

Entry Submitted: 03/09/2008
Entry Accepted: 03/09/2008
Entry Last Modified: 03/09/2008

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