Riemannian Multigrid Line Search for Low-Rank Problems
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Publication:4997383
DOI10.1137/20M1337430WikidataQ115246896 ScholiaQ115246896MaRDI QIDQ4997383
Bart Vandereycken, Marco Sutti
Publication date: 29 June 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.06976
Riemannian manifoldsroundoff errorline searchmultilevel optimizationlow-rank matricesoptimization on manifoldsretraction-based optimization
Computational methods for sparse matrices (65F50) Numerical optimization and variational techniques (65K10) Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Uses Software
Cites Work
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- Low-rank retractions: a survey and new results
- Partial differential equations: Modeling, analysis and numerical approximation
- Low-rank Riemannian eigensolver for high-dimensional Hamiltonians
- Riemannian Optimization for High-Dimensional Tensor Completion
- Low-Rank Matrix Completion by Riemannian Optimization
- Projection-like Retractions on Matrix Manifolds
- Manopt, a Matlab toolbox for optimization on manifolds
- A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations
- Tensor Spaces and Numerical Tensor Calculus
- Computational Methods for Linear Matrix Equations
- Geometric Methods on Low-Rank Matrix and Tensor Manifolds
- A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
- A Multigrid Method to Solve Large Scale Sylvester Equations
- Algorithm 851
- Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization
- A Line Search Multigrid Method for Large-Scale Nonlinear Optimization
- Recursive Trust-Region Methods for Multiscale Nonlinear Optimization
- A multilevel algorithm for solving the trust-region subproblem
- A multigrid approach to discretized optimization problems
- Jacobi--Davidson Method on Low-Rank Matrix Manifolds
- A Multilevel Technique for the Approximate Solution of Operator Lyapunov and Algebraic Riccati Equations
- Algorithm 941
- A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search
- Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
- A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem
- Low-Rank Optimization with Trace Norm Penalty
- The Mathematical Theory of Finite Element Methods
- The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints
- The Gradient Projection Method Along Geodesics
- Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure