Completely positive factorization by a Riemannian smoothing method

Abstract Copositive optimization is a special case of convex conic programming, and it consists optimizing linear function over the cone all completely positive matrices under constraints. provides powerful relaxations NP-hard quadratic problems or combinatorial problems, but there are still many open regarding copositive matrices. In this paper, we focus on one such problem; finding (CP) factorization for given matrix. We treat as nonsmooth Riemannian problem, i.e., minimization problem manifold. To solve present general smoothing framework solving show convergence to stationary point original problem. An advantage that can implement quickly with minimal effort by directly using existing standard smooth solvers, Manopt. Numerical experiments efficiency our method especially large-scale CP factorizations.