Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 1, pp. 93-105 (2000)

Minimal Spherical Shells and Linear Semi-infinite Optimization

Friedrich Junke; Olaf Sarges

Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany, e-mail: Juhnke@Mathematik.Uni-Magdeburg.de

Abstract: In this paper we prove some characterizing properties of the minimal shell of a convex body by means of linear semi-infinite optimization. Further we present a representation of the optimal solution of the corresponding optimization problem in dependence of the values of the support function of certain points of contact of the convex body and its minimal shell.

Keywords: linear semi-infinite optimization, minimal shell, convex bodies.

Classification (MSC2000): 52A40, 90C34

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