Title

Weak k-majorization and polyhedra

Document Type

Article

Publication Date

3-1-1998

Abstract

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. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Publication Title

Mathematical Programming, Series B

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