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Journal of Global Optimization

, Volume 35, Issue 2, pp 321–341 | Cite as

Computing the Minkowski Sum of Prisms

  • D. Pallaschke
  • J. Rosenmüller
Article

Abstract

Within this paper we study the Minkowski sum of prisms (“Cephoids”) in a finite dimensional vector space. For a vector \(a \in \mathbb{R}^n\) with positive components we write \({\bar{a}} = ({1\over \bar{a}_1}, \cdots , {1\over \bar{a}_n})\) and denote by \(\prod = \prod^{\bar{a}} = \{x \in \mathbb{R}^n | \langle \bar{a}, {\bf x} \rangle \leqslant 1, {\bf x} \geqslant 0 \}\) the associated prism. We provide a representation of a finite sum of prisms in terms of inequalities.

Keywords

convex analysis minkowski sum polytopes 

Mathematics Subject Classifications (2000)

52A07 26A27 90C08 

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Institut für Statistik und Mathem. WirtschaftstheorieUniversität KarlsruheKarlsruheGermany
  2. 2.Institut für Mathematische WirtschaftsforschungUniversität BielefeldBielefeldGermany

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