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.