A matrix-free implementation of Riemannian Newton's method on the Stiefel manifold

DOI10.1007/s11590-016-1090-9zbMath1386.90141OpenAlexW2532990506WikidataQ115377844 ScholiaQ115377844MaRDI QIDQ1686561

Hiroyuki Sato, Kensuke Aihara

Publication date: 15 December 2017

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-016-1090-9

zbMATH Keywords

linear systemsingular value decompositionStiefel manifoldRiemannian Newton's methodmatrix-free Krylov subspace method

Mathematics Subject Classification ID

Nonlinear programming (90C30) Methods of quasi-Newton type (90C53) Programming in abstract spaces (90C48)

Related Items (7)

MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection ⋮ An efficient damped Newton-type algorithm with globalization strategy on Riemannian manifolds ⋮ Second order optimality on orthogonal Stiefel manifolds ⋮ Cholesky QR-based retraction on the generalized Stiefel manifold ⋮ Effective algorithms for solving trace minimization problem in multivariate statistics ⋮ Newton's method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils ⋮ Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method

Cites Work

• Intrinsic representation of tangent vectors and vector transports on matrix manifolds
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• The Geometry of Algorithms with Orthogonality Constraints
• A Riemannian Optimization Approach to the Matrix Singular Value Decomposition
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