Riemannian optimization on the space of covariance matrices

In many modern statistical applications the data complexity may require techniques that exploit the geometrical properties of the objects of interest. For example, if the parameter of interest is a covariance matrix, the parameter space is nonEuclidean. In this work we focus on this notable example and study the Riemannian manifold of symmetric and positive definite matrices. Specifically an optimization procedures which takes into account such geometrical properties is described and tested via simulations