Riemannian conjugate gradient method for complex singular value decomposition problem

In this paper, a Riemannian conjugate gradient method for a Riemannian optimization problem related to the singular value decomposition of a complex matrix is developed. The proposed algorithm is globally convergent, unlike Newton´s method. However, Newton´s method for this problem is locally quadratically convergent. With this in mind, the proposed conjugate gradient method is combined with Newton´s method to produce a hybrid algorithm, which is globally and quadratically convergent in practice.