117 citations · 429 across the 15 of their papers we have counts for
15 papers
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…
Riemannian conjugate gradient methods: General framework and specific algorithms with convergence analyses
Hiroyuki Sato
This paper proposes a novel general framework of Riemannian conjugate gradient methods, that is, conjugate gradient methods on Riemannian manifolds. The conjugate gradient methods…
Riemannian optimal identification method for linear systems with symmetric positive-definite matrix
Kazuhiro Sato, Hiroyuki Sato, Tobias Damm
This study develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multi-agent network systems, and temperature dynamics i…
Structure-preserving optimal model reduction based on Riemannian trust-region method
Kazuhiro Sato, Hiroyuki Sato
This paper studies stability and symmetry preserving optimal model reduction problems of linear systems which include linear gradient systems as a special case. The problem i…
Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis
Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riema…
Riemannian stochastic variance reduced gradient algorithm with retraction and vector transport
Hiroyuki Sato, Hiroyuki Kasai, Bamdev Mishra
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This pape…
Riemannian stochastic variance reduced gradient on Grassmann manifold
Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel…
A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions
Hiroyuki Sato
This article describes a new Riemannian conjugate gradient method and presents a global convergence analysis. The existing Fletcher-Reeves-type Riemannian conjugate gradient method…
Riemannian Newton-type methods for joint diagonalization on the Stiefel manifold with application to independent component analysis
Hiroyuki Sato
The joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. This problem can be formulated as an optimizati…
A new, globally convergent Riemannian conjugate gradient method
Hiroyuki Sato, Toshihiro Iwai
This article deals with the conjugate gradient method on a Riemannian manifold with interest in global convergence analysis. The existing conjugate gradient algorithms on a manifol…