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. … Read more

Completely Positive Factorization by a Riemannian Smoothing Method

Copositive optimization is a special case of convex conic programming, and it optimizes a linear function over the cone of all completely positive matrices under linear constraints. Copositive optimization provides powerful relaxations of NP-hard quadratic problems or combinatorial problems, but there are still many open problems regarding copositive or completely positive matrices. In this paper, … Read more