Weak k-Majorization and Polyhedra

2018-07-01T00:45:28Z (GMT) by Geir Dahl Francois Margot
For integers k and n with k ≤ n a vector x ∈ ℝ<sup>n</sup> is said to be weakly k-majorized by a vector q ∈ ℝ<sup>k</sup> 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