cayley transform – Optimization Online

Riemannian Optimization on the Symplectic Stiefel Manifold

Published: 2020/06/26

Constrained Nonlinear Optimization cayley transform, quasi-geodesic, riemannian optimization, symplectic stiefel manifold

The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p,2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$. When $p=n$, it reduces to the well-known set of $2n\times 2n$ symplectic matrices. Optimization problems on $\mathrm{Sp}(2p,2n)$ find applications in various areas, such as optics, quantum physics, numerical linear algebra and model order … Read more

A Riemannian conjugate gradient method for optimization on the Stiefel manifold

Published: 2016/09/04, Updated: 2016/11/20

Xiaojing Zhu

Applications - Science and Engineering, Linear, Cone and Semidefinite Programming, Nonlinear Optimization cayley transform, conjugate gradient method, retraction, riemannian optimization, stiefel manifold, vector transport

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 … Read more