Weak k-majorization and polyhedra

Authors

Geir Dahl, Universitetet i Oslo
François Margot, Michigan Technological University

Document Type

Article

Publication Date

3-1998

Department

Department of Mathematical Sciences

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.

Publisher's Statement

© 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V. Publisher’s version of record: https://doi.org/10.1007/BF01584843

Publication Title

Mathematical Programming, Series B

Recommended Citation

Dahl, G., & Margot, F. (1998). Weak k-majorization and polyhedra. Mathematical Programming, Series B, 81(1), 37-53. http://doi.org/10.1007/BF01584843
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4327