4 citations · 4 across the 6 of their papers we have counts for
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Riemannian optimization framework on the generalized quaternionic Stiefel Manifold
Hiroyuki Sato
This paper introduces the generalized quaternionic Stiefel manifold and studies its geometry for Riemannian optimization. We clarify its relationships with existing manifolds, espe…
Second-order geometry and Riemannian Newton-type methods for optimization on the indefinite Stiefel manifold
Hiroyuki Sato
This paper investigates the second-order geometry of the indefinite Stiefel manifold and derives explicit formulas for the Levi-Civita connection and the Riemannian Hessian under t…
Nonlinear conjugate gradient method for vector optimization on Riemannian manifolds with retraction and vector transport
Kangming Chen, Ellen H. Fukuda, Hiroyuki Sato
In this paper, we propose nonlinear conjugate gradient methods for vector optimization on Riemannian manifolds. The concepts of Wolfe and Zoutendjik conditions are extended for Rie…
Modified Armijo line search in optimization on Riemannian submanifolds with reduced computational cost
Hiroyuki Sato, Yuya Yamakawa, Kensuke Aihara
For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the A…
Global Convergence of Hager-Zhang type Riemannian Conjugate Gradient Method
Hiroyuki Sakai, Hiroyuki Sato, Hideaki Iiduka
This paper presents the Hager-Zhang (HZ)-type Riemannian conjugate gradient method that uses the exponential retraction. We also present global convergence analyses of our proposed…
Riemannian optimization on unit sphere with -norm and its applications
Hiroyuki Sato
This paper deals with Riemannian optimization on the unit sphere in terms of -norm with general . As a Riemannian submanifold of the Euclidean space, the geometry of the…