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Optimization algorithms on matrix manifolds

1, 2008

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Analysis and design of nonlinear resonances via singularity theory

Journal of sound and vibration, 2017-03, Vol.392, p.295-306

2017

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Low-Rank Optimization with Trace Norm Penalty

SIAM journal on optimization, 2013-01, Vol.23 (4), p.2124-2149

2013

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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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Consensus on nonlinear spaces

Annual reviews in control, 2011-04, Vol.35 (1), p.56-64

Sepulchre, R.

2011

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Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation

Acta applicandae mathematicae, 2004-01, Vol.80 (2), p.199-220

2004

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Contraction of monotone phase-coupled oscillators

Systems & control letters, 2012-11, Vol.61 (11), p.1097-1102

2012

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A spectral characterization of nonlinear normal modes

Journal of sound and vibration, 2016-09, Vol.377, p.284-301

2016

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A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces

SIAM review, 2002-03, Vol.44 (1), p.57-73

2002

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Cubically convergent iterations for invariant subspace computation

SIAM journal on matrix analysis and applications, 2004-01, Vol.26 (1), p.70-96

2004

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Nonlinear analysis of cardiac rhythm fluctuations using DFA method

Physica A, 1999-10, Vol.272 (1), p.235-244

1999

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Differential positivity with respect to cones of rank k ≥ 2

IFAC-PapersOnLine, 2017, Vol.50 (1), p.7439-7444

2017

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On differentially dissipative dynamical systems

IFAC Proceedings Volumes, 2013, Vol.46 (23), p.15-20

2013

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Invariant Differential Positivity and Consensus on Lie Groups

IFAC-PapersOnLine, 2016, Vol.49 (18), p.630-635

2016

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Path-complete positivity of switching systems

IFAC-PapersOnLine, 2017, Vol.50 (1), p.4558-4563

2017

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Stabilization and Disturbance Attenuation of Nonlinear Systems Using Dissipativity Theory

European journal of control, 2002, Vol.8 (5), p.408-431

2002

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Differentially passive circuits that switch and oscillate

IFAC-PapersOnLine, 2018, Vol.51 (13), p.19-24

2018

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Oscillators as Systems and Synchrony as a Design Principle

Current Trends in Nonlinear Systems and Control, p.123-141

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Consensus on Nonlinear Spaces

IFAC Proceedings Volumes, 2010-09, Vol.43 (14), p.1029-1039

Sepulchre, R.

2010

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Boundedness Properties For Time-Varying Nonlinear Systems

SIAM journal on control and optimization, 2000-01, Vol.39 (5), p.1408-1422

2000

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Notation Conventions

Optimization Algorithms on Matrix Manifolds, 2009, p.xv-xvi

2009

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List of Algorithms

Optimization Algorithms on Matrix Manifolds, 2009, p.xi-xii

2009

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Matrix Manifolds: First-Order Geometry

Optimization Algorithms on Matrix Manifolds, 2009, p.17-53

2009

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A Constellation of Superlinear Algorithms

Optimization Algorithms on Matrix Manifolds, 2009, p.168-188

2009

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Matrix Manifolds: Second-Order Geometry

Optimization Algorithms on Matrix Manifolds, 2009, p.91-110

2009

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Optimization algorithms on matrix manifolds

Analysis and design of nonlinear resonances via singularity theory

Low-Rank Optimization with Trace Norm Penalty

Low-Rank Optimization on the Cone of Positive Semidefinite Matrices

Consensus on nonlinear spaces

Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation

Contraction of monotone phase-coupled oscillators

A spectral characterization of nonlinear normal modes

A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces

Cubically convergent iterations for invariant subspace computation

Nonlinear analysis of cardiac rhythm fluctuations using DFA method

Differential positivity with respect to cones of rank k ≥ 2

On differentially dissipative dynamical systems

Invariant Differential Positivity and Consensus on Lie Groups

Path-complete positivity of switching systems

Stabilization and Disturbance Attenuation of Nonlinear Systems Using Dissipativity Theory

Differentially passive circuits that switch and oscillate

Oscillators as Systems and Synchrony as a Design Principle

Consensus on Nonlinear Spaces

Boundedness Properties For Time-Varying Nonlinear Systems

Notation Conventions

List of Algorithms

Matrix Manifolds: First-Order Geometry

A Constellation of Superlinear Algorithms

Matrix Manifolds: Second-Order Geometry

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