A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors
type: Item
instance of: scholarly article
title: A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors
zbMATH Open document ID: 1503.65130
author: Zhou Sheng
author: Weiwei Yang
author: Jie Wen
published in: Applied Numerical Mathematics
publication date: 2022-10-18T00:00:00Z
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65F99
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 7603717
zbMATH Keywords: Riemannian gradient
zbMATH Keywords: symmetric tensor
zbMATH Keywords: tensor approximation
zbMATH Keywords: global convergence
zbMATH Keywords: Łojasiewicz gradient inequality
describes a project that uses: Manopt
Wikidata QID: Q113880028
MaRDI profile type: Publication
full work available at URL: j.apnum.2022.08.005
OpenAlex ID: W4293014333
cites work: Projection-like retractions on matrix manifolds
cites work: Convergence of the Iterates of Descent Methods for Analytic Cost Functions
cites work: Q5433140
cites work: Two-Point Step Size Gradient Methods
cites work: Manopt, a Matlab toolbox for optimization on manifolds
cites work: On the Tensor SVD and the Optimal Low Rank Orthogonal Approximation of Tensors
cites work: Independent component analysis, a new concept?
cites work: Contrasts, independent component analysis, and blind deconvolution
cites work: A Multilinear Singular Value Decomposition
cites work: On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
cites work: Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm
cites work: A New First-Order Algorithmic Framework for Optimization Problems with Orthogonality Constraints
cites work: An inexact augmented Lagrangian method for computing strongly orthogonal decompositions of tensors
cites work: A Riemannian BFGS Method for Nonconvex Optimization Problems
cites work: Jacobi algorithm for the best low multilinear rank approximation of symmetric tensors
cites work: Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme
cites work: Differential-geometric Newton method for the best rank-\((R _{1}, R _{2}, R _{3})\) approximation of tensors
cites work: On the best rank-1 approximation of higher-order supersymmetric tensors
cites work: Orthogonal tensor decompositions
cites work: Tensor Decompositions and Applications
cites work: Shifted Power Method for Computing Tensor Eigenpairs
cites work: A splitting method for orthogonality constrained problems
cites work: Globally Convergent Jacobi-Type Algorithms for Simultaneous Orthogonal Symmetric Tensor Diagonalization
cites work: Q5157448
cites work: A Jacobi-Type Method for Computing Orthogonal Tensor Decompositions
cites work: Semidefinite Relaxations for Best Rank-1 Tensor Approximations
cites work: Numerical Optimization
cites work: Symmetric orthogonal approximation to symmetric tensors with applications to image reconstruction
cites work: Tensor eigenvalues and their applications
cites work: Monotonically convergent algorithms for symmetric tensor approximation
cites work: A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions
cites work: A new, globally convergent Riemannian conjugate gradient method
cites work: Krylov-type methods for tensor computations.I
cites work: Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
cites work: Convergence Results for Projected Line-Search Methods on Varieties of Low-Rank Matrices Via Łojasiewicz Inequality
cites work: Approximate Matrix and Tensor Diagonalization by Unitary Transformations: Convergence of Jacobi-Type Algorithms
cites work: A feasible method for optimization with orthogonality constraints
cites work: Rank-one approximation to high order tensors
cites work: The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems
DOI: 10.1016/J.APNUM.2022.08.005
description: scientific article; zbMATH DE number 7603717