On the polyhedral cones of convex and concave vectors

Abstract

Convex or concave sequences of n positive terms, viewed as vectors in n-space, constitute convex cones with 2n − 2 and n extreme rays, respectively. Explicit description is given of vectors spanning these extreme rays, as well as of non-singular linear transformations between the positive orthant and the simplicial cones formed by the positive concave vectors. The simplicial cones of monotone convex and concave vectors can be described similarly.