Intrinsic representation of tangent vectors and vector transports on matrix manifolds

DOI10.1007/s00211-016-0848-4zbMath1366.65062OpenAlexW2541805425MaRDI QIDQ530089

Wen Huang, Pierre-Antoine Absil, Kyle A. Gallivan

Publication date: 9 June 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-016-0848-4

zbMATH Keywords

algorithmconvergencenumerical examplesStiefel manifoldRiemannian manifoldsGrassmann manifoldquasi-Newton methodsBrockett cost functionisometric vector transport

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Methods of quasi-Newton type (90C53) Programming in abstract spaces (90C48)

Related Items (14)

Transportless conjugate gradient for optimization on Stiefel manifold ⋮ A limited-memory Riemannian symmetric rank-one trust-region method with a restart strategy ⋮ A matrix-free implementation of Riemannian Newton's method on the Stiefel manifold ⋮ An image inpainting algorithm using exemplar matching and low-rank sparse prior ⋮ Solving PhaseLift by Low-Rank Riemannian Optimization Methods for Complex Semidefinite Constraints ⋮ A Riemannian Proximal Newton Method ⋮ A Riemannian BFGS Method Without Differentiated Retraction for Nonconvex Optimization Problems ⋮ Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds ⋮ An inexact Riemannian proximal gradient method ⋮ A brief introduction to manifold optimization ⋮ Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds ⋮ A Riemannian conjugate gradient method for optimization on the Stiefel manifold ⋮ On matrix exponentials and their approximations related to optimization on the Stiefel manifold ⋮ Blind Deconvolution by a Steepest Descent Algorithm on a Quotient Manifold

Uses Software

• LAPACK
• Matrix Means Toolbox
• RTRMC

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions
• Riemannian optimization for registration of curves in elastic shape analysis
• Low-rank retractions: a survey and new results
• Computing the Karcher mean of symmetric positive definite matrices
• A Riemannian symmetric rank-one trust-region method
• Trust-region methods on Riemannian manifolds
• Low-Rank Matrix Completion by Riemannian Optimization
• On the Convergence of Gradient Descent for Finding the Riemannian Center of Mass
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
• A Broyden Class of Quasi-Newton Methods for Riemannian Optimization
• Introduction to Topological Manifolds
• Newton's method on Riemannian manifolds and a geometric model for the human spine
• A Riemannian BFGS Method for Nonconvex Optimization Problems
• Geodesic finite elements for Cosserat rods
• The Geometry of Algorithms with Orthogonality Constraints
• Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
• A new, globally convergent Riemannian conjugate gradient method
• A Geometric Approach to Low-Rank Matrix Completion
• Solving PhaseLift by Low-Rank Riemannian Optimization Methods for Complex Semidefinite Constraints

This page was built for publication: Intrinsic representation of tangent vectors and vector transports on matrix manifolds