Interiors of completely positive cones

Abstract

A symmetric matrix A is completely positive (CP) if there exists an entrywise nonnegative matrix B such that $$A = BB^T$$A=BBT. We characterize the interior of the CP cone. A semidefinite algorithm is proposed for checking whether a matrix is in the interior of the CP cone, and its properties are studied. A CP-decomposition of a matrix in Dickinson's form can be obtained if it is an interior of the CP cone. Some computational experiments are also presented.