A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors

In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same express...

Full description

Saved in:
Bibliographic Details
Published in:Applied numerical mathematics Vol. 182; pp. 235 - 247
Main Authors: Sheng, Zhou, Yang, Weiwei, Wen, Jie
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2022
Subjects:
Global convergence
Riemannian gradient
Symmetric tensor
Tensor approximation
Łojasiewicz gradient inequality
Riemannian gradient
Global convergence
Tensor approximation
Łojasiewicz gradient inequality
Symmetric tensor
ISSN:0168-9274, 1873-5460
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same expression as the Polar decomposition. We establish that the global convergence of our algorithm. Preliminary results show that the computational advantage of our algorithm.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2022.08.005