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Weakk-majorization and polyhedra

Mathematical Programming volume 81, pages 37–53 (1998)Cite this article

Abstract

For integersk andn withk ⩽ n a vectorx ∈ ℝ n is said to be weaklyk-majorized by a vectorq ∈ ℝ k if the sum of ther largest components ofx does not exceed the sum of ther largest components ofq, forr = 1,⋯,k. For a givenq the set of vectors weaklyk-majorized byq defines a polyhedronP(q; k). We determine the vertices of bothP(q; k) and its integer hullQ(q; k). Furthermore a complete and nonredundant linear description ofQ(q; k) is given. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

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Authors and Affiliations

  1. Institute of Informatics, University of Oslo, Blindern, P.O. Box 1080, 0316, Oslo, Norway

    Geir Dahl

  2. Department of Mathematical Sciences, Michigan Technological University, 49931-1295, Houghton, MI, USA

    François Margot

Authors
  1. Geir Dahl
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  2. François Margot
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Dahl, G., Margot, F. Weakk-majorization and polyhedra. Mathematical Programming 81, 37–53 (1998). https://doi.org/10.1007/BF01584843

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  • DOI: https://doi.org/10.1007/BF01584843

Keywords

  • Majorization
  • Polyhedra

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