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Optimization algorithms on matrix manifolds

1, 2008

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Global rates of convergence for nonconvex optimization on manifolds

IMA journal of numerical analysis, 2019-01, Vol.39 (1), p.1-33

2019

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Projection-like Retractions on Matrix Manifolds

SIAM journal on optimization, 2012-01, Vol.22 (1), p.135-158

2012

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A Riemannian rank-adaptive method for low-rank matrix completion

Computational optimization and applications, 2022-01, Vol.81 (1), p.67-90

2022

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Low-rank matrix completion via preconditioned optimization on the Grassmann manifold

Linear algebra and its applications, 2015-06, Vol.475, p.200-239

2015

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Two algorithms for orthogonal nonnegative matrix factorization with application to clustering

Neurocomputing (Amsterdam), 2014-10, Vol.141, p.15-25

2014

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Robust Low-Rank Matrix Completion by Riemannian Optimization

SIAM journal on scientific computing, 2016-01, Vol.38 (5), p.S440-S460

2016

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Low-rank plus sparse decomposition for exoplanet detection in direct-imaging ADI sequences: The LLSG algorithm

Astronomy and astrophysics (Berlin), 2016-05, Vol.589, p.A54

2016

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Riemannian Optimization on the Symplectic Stiefel Manifold

SIAM journal on optimization, 2021-01, Vol.31 (2), p.1546-1575

2021

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Generalized Linear Models to Forecast Malaria Incidence in Three Endemic Regions of Senegal

International journal of environmental research and public health, 2023-07, Vol.20 (13), p.6303

2023

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A Grassmann manifold handbook: basic geometry and computational aspects

Advances in computational mathematics, 2024-02, Vol.50 (1), Article 6

2024

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Low-rank retractions: a survey and new results

Computational optimization and applications, 2015-09, Vol.62 (1), p.5-29

2015

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Quotient Geometry with Simple Geodesics for the Manifold of Fixed-Rank Positive-Semidefinite Matrices

SIAM journal on matrix analysis and applications, 2020-01, Vol.41 (1), p.171-198

2020

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BEST LOW MULTILINEAR RANK APPROXIMATION OF HIGHER-ORDER TENSORS, BASED ON THE RIEMANNIAN TRUST-REGION SCHEME

SIAM journal on matrix analysis and applications, 2011, Vol.32 (1), p.115-135

2011

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A Riemannian BFGS Method Without Differentiated Retraction for Nonconvex Optimization Problems

SIAM journal on optimization, 2018-01, Vol.28 (1), p.470-495

2018

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An Apocalypse-Free First-Order Low-Rank Optimization Algorithm with at Most One Rank Reduction Attempt per Iteration

SIAM journal on matrix analysis and applications, 2023-09, Vol.44 (3), p.1421-1435

2023

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On the Continuity of the Tangent Cone to the Determinantal Variety

Set-valued and variational analysis, 2022-06, Vol.30 (2), p.769-788

2022

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Low-Rank Optimization on the Cone of Positive Semidefinite Matrices

SIAM journal on optimization, 2010-01, Vol.20 (5), p.2327-2351

2010

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Data Fitting on Manifolds with Composite Bézier-Like Curves and Blended Cubic Splines

Journal of mathematical imaging and vision, 2019-06, Vol.61 (5), p.645-671

2019

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Trust-Region Methods on Riemannian Manifolds

Foundations of computational mathematics, 2007-07, Vol.7 (3), p.303-330

2007

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A Riemannian symmetric rank-one trust-region method

Mathematical programming, 2015-05, Vol.150 (2), p.179-216

2015

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Intrinsic representation of tangent vectors and vector transports on matrix manifolds

Numerische Mathematik, 2017-06, Vol.136 (2), p.523-543

2017

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On a minimum enclosing ball of a collection of linear subspaces

Linear algebra and its applications, 2021-09, Vol.625, p.248-278

2021

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Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors

SIAM journal on matrix analysis and applications, 2013-01, Vol.34 (2), p.651-672

2013

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A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds

Foundations of computational mathematics, 2012-02, Vol.12 (1), p.49-73

2012

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Optimization algorithms on matrix manifolds

Global rates of convergence for nonconvex optimization on manifolds

Projection-like Retractions on Matrix Manifolds

A Riemannian rank-adaptive method for low-rank matrix completion

Low-rank matrix completion via preconditioned optimization on the Grassmann manifold

Two algorithms for orthogonal nonnegative matrix factorization with application to clustering

Robust Low-Rank Matrix Completion by Riemannian Optimization

Low-rank plus sparse decomposition for exoplanet detection in direct-imaging ADI sequences: The LLSG algorithm

Riemannian Optimization on the Symplectic Stiefel Manifold

Generalized Linear Models to Forecast Malaria Incidence in Three Endemic Regions of Senegal

A Grassmann manifold handbook: basic geometry and computational aspects

Low-rank retractions: a survey and new results

Quotient Geometry with Simple Geodesics for the Manifold of Fixed-Rank Positive-Semidefinite Matrices

BEST LOW MULTILINEAR RANK APPROXIMATION OF HIGHER-ORDER TENSORS, BASED ON THE RIEMANNIAN TRUST-REGION SCHEME

A Riemannian BFGS Method Without Differentiated Retraction for Nonconvex Optimization Problems

An Apocalypse-Free First-Order Low-Rank Optimization Algorithm with at Most One Rank Reduction Attempt per Iteration

On the Continuity of the Tangent Cone to the Determinantal Variety

Low-Rank Optimization on the Cone of Positive Semidefinite Matrices

Data Fitting on Manifolds with Composite Bézier-Like Curves and Blended Cubic Splines

Trust-Region Methods on Riemannian Manifolds

A Riemannian symmetric rank-one trust-region method

Intrinsic representation of tangent vectors and vector transports on matrix manifolds

On a minimum enclosing ball of a collection of linear subspaces

Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors

A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds

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