A Riemannian rank-adaptive method for low-rank optimization

This paper presents an algorithm that solves optimization problems on a matrix manifold $\mathcal{M} \subseteq \mathbb{R}^{m \times n}$ with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted … Read more