Duality of Ellipsoidal Approximations via Semi-Infinite Programming

Authors:
Filiz Gürtuna
Affiliations:
gurtuna1@math.umbc.edu
Venue:
SIAM Journal on Optimization
Year:
2009

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Abstract

In this paper, 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.