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Weak k-Majorization and Polyhedra

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journal contribution
posted on 01.01.2010 by Geir Dahl, Francois Margot
For integers k and n with k ≤ n a vector x ∈ ℝn is said to be weakly k-majorized by a vector q ∈ ℝk if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1,⋯,k. For a given q the set of vectors weakly k-majorized by q defines a polyhedron P(q; k). We determine the vertices of both P(q; k) and its integer hull Q(q; k). Furthermore a complete and nonredundant linear description of Q(q; k) is given


Publisher Statement

This is an Accepted Manuscript of an article published by Taylor & Francis Group available online at: http://www.tandfonline.com/10.1080/1529886090310684].