Interiors of completely positive cones

TL;DR

This paper characterizes the interior of the completely positive cone, proposes a semidefinite algorithm for checking interior membership, and demonstrates how to obtain CP-decompositions for interior matrices with computational experiments.

Contribution

It provides a characterization of the interior of the CP cone and introduces a semidefinite algorithm for interior verification and decomposition.

Findings

The interior of the CP cone is characterized.

A semidefinite algorithm effectively checks interior membership.

Computational experiments validate the proposed methods.

Abstract

A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $A = BB^T$. We characterize the interior of the CP cone. A semidefinite algorithm is proposed for checking interiors 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.