Computing the completely positive factorization via alternating minimization

In this article, we propose a novel alternating minimization scheme for finding completely positive factorizations. In each iteration, our method splits the original factorization problem into two optimization subproblems, the first one being a orthogonal procrustes problem, which is taken over the orthogoal group, and the second one over the set of entrywise positive matrices. We present both a convergence analysis of the method and favorable numerical results.