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Calculus rules for combinations of ellipsoids and applications

Published online by Cambridge University Press:  17 April 2009

Alberto Seeger
Alberto Seeger
Affiliation:
Université d'Avignon, Département de Mathématiques 84000 Avignon, France
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Abstract

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We derive formulas for the Minkowski sum, the convex hull, the intersection, and the inverse sum of a finite family of ellipsoids. We show how these formulas can be used to obtain inner and outer ellipsoidal approximations of a convex polytope.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 1 , February 1993 , pp. 1 - 12
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Hiriart-Urruty, J.-B. and Seeger, A., ‘Calculus rules on a new set-valued second-order derivative for convex functions’, Nonlinear Anal.: Th. Meth and Appl. 13 (1989), 721–738.Google Scholar
[2]Kurshanski, A.B. and Valyi, I., ‘Ellipsoidal techniques: guaranteed state estimation’, Working paper, (International Institute for Applied Systems Analysis, Laxenburg, Austria, 1991).Google Scholar
[3]Masure, M.L., Analyse variationnelle des formes quadratiques convexes, Thesis (University Paul Sabatier, Toulouse, 1986).Google Scholar
[4]Masure, M.L., ‘L'addition parallèle d'opérateurs interprétée comme inf-convolution de formes quadratiques convexes’, Math. Modelling Numer. Anal. 20 (1986), 497–515.Google Scholar
[5]Rockafellar, R.T., Convex analysis (Princeton Univ.Press, New Jersey, 1970).CrossRefGoogle Scholar
[6]Seeger, A., ‘Direct and inverse addition in convex analysis and applications’, J. Math. Anal. Appl. 148 (1990), 317–349.CrossRefGoogle Scholar