Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold

A Riemannian conjugate gradient method for optimization on the Stiefel manifold

In this paper we propose a new Riemannian conjugate gradient method for optimization on the Stiefel manifold. We introduce two novel vector transports associated with the retraction constructed by the Cayley transform. Both of them satisfy the Ring-Wirth nonexpansive condition, which is fundamental for convergence analysis of Riemannian conjugate gradient methods, and one of them is also isomet...

On a class of paracontact Riemannian manifold

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

A Matrix-Algebraic Algorithm for the Riemannian Logarithm on the Stiefel Manifold under the Canonical Metric

Systems Engineering: Optimization on Stiefel Manifold for MIMO System

Applications of multiple input and multiple output (MIMO) with Stiefel manifold are growing in the next generation communications and their system engineering developments. These applications need to be optimized efficiently with less complexity and cost. In this research, optimization problems in MIMO systems using Stiefel manifold are considered. As far as general manifolds are concerned, opt...

Low-rank tensor completion: a Riemannian manifold preconditioning approach

We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry that exists in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian opt...