Low-rank retractions: a survey and new results

DOI10.1007/s10589-014-9714-4zbMath1334.90202OpenAlexW1972710290MaRDI QIDQ496216

Ivan V. Oseledets, Pierre-Antoine Absil

Publication date: 21 September 2015

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-014-9714-4

zbMATH Keywords

retractionlow-rank matrix completionlow-rank manifoldlow-rank optimization

Mathematics Subject Classification ID

Programming in abstract spaces (90C48) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02)

Related Items (23)

Riemannian Conjugate Gradient Methods: General Framework and Specific Algorithms with Convergence Analyses ⋮ Automatic Differentiation for Riemannian Optimization on Low-Rank Matrix and Tensor-Train Manifolds ⋮ Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation ⋮ Low-rank tensor methods for partial differential equations ⋮ A framework of regularized low-rank matrix models for regression and classification ⋮ Fast gradient method for low-rank matrix estimation ⋮ Stable Rank-Adaptive Dynamically Orthogonal Runge–Kutta Schemes ⋮ Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Mini-workshop: Computational optimization on manifolds. Abstracts from the mini-workshop held November 15--21, 2020 (online meeting) ⋮ Jacobi--Davidson Method on Low-Rank Matrix Manifolds ⋮ Time Integration of Tree Tensor Networks ⋮ Time Integration of Rank-Constrained Tucker Tensors ⋮ Intrinsic representation of tangent vectors and vector transports on matrix manifolds ⋮ Riemannian conjugate gradient methods with inverse retraction ⋮ Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values ⋮ Proximal Gradient Method for Nonsmooth Optimization over the Stiefel Manifold ⋮ Quotient Geometry with Simple Geodesics for the Manifold of Fixed-Rank Positive-Semidefinite Matrices ⋮ Robust Low-Rank Matrix Completion by Riemannian Optimization ⋮ Riemannian Optimization for High-Dimensional Tensor Completion ⋮ Unnamed Item ⋮ Projection methods for dynamical low-rank approximation of high-dimensional problems ⋮ Riemannian Multigrid Line Search for Low-Rank Problems

Uses Software

• Manopt

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Low-rank tensor completion by Riemannian optimization
• Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries
• Fixed-rank matrix factorizations and Riemannian low-rank optimization
• Trust-region methods on Riemannian manifolds
• A projector-splitting integrator for dynamical low-rank approximation
• Low-Rank Matrix Completion by Riemannian Optimization
• Projection-like Retractions on Matrix Manifolds
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
• Manopt, a Matlab toolbox for optimization on manifolds
• Newton's method on Riemannian manifolds and a geometric model for the human spine
• Low-Rank Optimization with Trace Norm Penalty
• Dynamical Low‐Rank Approximation
• The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints
• The Gradient Projection Method Along Geodesics

This page was built for publication: Low-rank retractions: a survey and new results