Xiaojing Zhu – Optimization Online

Accelerated gradient methods on the Grassmann and Stiefel manifolds

Published: 2022/07/09, Updated: 2023/09/04

Constrained Nonlinear Optimization accelerated gradient, global rate of convergence, grassmann manifold, riemannian optimization, stiefel manifold

In this paper we extend a nonconvex version of Nesterov’s accelerated gradient (AG) method to optimization over the Grassmann and Stiefel manifolds. We propose an exponential-based AG algorithm for the Grassmann manifold and a retraction-based AG algorithm that exploits the Cayley transform for both of the Grassmann and Stiefel manifolds. Under some mild assumptions, we … Read more

Riemannian conjugate gradient methods with inverse retraction

Published: 2020/05/17, Updated: 2020/09/04

Hiroyuki Sato

Xiaojing Zhu

Nonlinear Optimization conjugate gradient method, fixed-rank manifold, inverse retraction, retraction, riemannian optimization, stiefel manifold

We propose a new class of Riemannian conjugate gradient (CG) methods, in which inverse retraction is used instead of vector transport for search direction construction. In existing methods, differentiated retraction is often used for vector transport to move the previous search direction to the current tangent space. However, a different perspective is adopted here, motivated … Read more