An improved characterisation of the interior of the completely positive cone

Abstract

A symmetric matrix is defined to be completely positive if it allows a factorisation BBT , where B is an entrywise nonnegative matrix. This set is useful in certain optimisation problems. The interior of the completely positive cone has previously been characterised by Du¨r and Still [M. Du¨r and G. Still, Interior points of the completely positive cone, Electronic Journal of Linear Algebra, 17:48–53, 2008]. In this paper, we introduce the concept of the set of zeros in the nonnegative orthant for a quadratic form, and use the properties of this set to give a more relaxed characterisation of the interior of the completely positive cone.