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Smooth, non-convex optimization problems on Riemannian manifolds occur in machine learning as a result of orthonormality, rank or positivity constraints.
The geometry of algorithms with orthogonality constraints
A. Edelman, T.A. Arias, and S.T. Smith · 1998
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Numerical Optimization
J. Nocedal and S. Wright · 1999
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Newton’s method on Riemannian manifolds and a geometric model for the human spine
R. Adler, J. Dedieu, J. Margulies, M. Martens, and M. Shub · 2002
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Joint diagonalization on the oblique manifold for independent component analysis
P.-A. Absil and K. A. Gallivan · 2006
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Cubic regularization of newton method and its global performance
Y. Nesterov and B. T. Polyak · 2006
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Trust-region methods on Riemannian manifolds
P.-A. Absil, C. G. Baker, and K. A. Gallivan · 2007
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Optimization Algorithms on Matrix Manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2008
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Statistical analysis on stiefel and grassmann manifolds with applications in computer vision
Pavan Turaga, Ashok Veeraraghavan, and Rama Chellappa · 2008
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Optimization on manifolds: Methods and applications
P. A. Absil, R. Mahony, and R. Sepulchre · 2010
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Projection-like retractions on matrix manifolds
P.-A. Absil and J. Malick · 2012
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Stochastic gradient descent on Riemannian manifolds
S. Bonnabel · 2013
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On the saddle point problem for non-convex optimization
Razvan Pascanu, Yann N. Dauphin, Surya Ganguli, and Yoshua Bengio · 2014
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Escaping from saddle points–online stochastic gradient for tensor decomposition
Rong Ge, Furong Huang, Chi Jin, and Yang Yuan · 2015
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Robust low-rank matrix completion by riemannian optimization
Leopold Cambier and P. A. Absil · 2016
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The power of normalization: Faster evasion of saddle points
Kfir Y. Levy · 2016
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Complete dictionary recovery over the sphere I: Overview and the geometric picture
Ju Sun, Qing Qu, and John Wright · 2016
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Riemannian SVRG: Fast stochastic optimization on Riemannian manifolds
Hongyi Zhang, Sashank J. Reddi, and Suvrit Sra · 2016
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Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
Accelerated gradient descent escapes saddle points faster than gradient descent
Chi Jin, Praneeth Netrapalli, and Michael I. Jordan · 2018
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Escaping saddle points in constrained optimization
Aryan Mokhtari, Asuman Ozdaglar, and Ali Jadbabaie · 2018
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Smoothed analysis of the low-rank approach for smooth semidefinite programs
T. Pumir, S. Jelassi, and N. Boumal · 2018
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Adaptive stochastic gradient langevin dynamics: Taming convergence and saddle point escape time
Hejian Sang and Jia Liu · 2018
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Escaping saddle points efficiently in equality-constrained optimization problems
Yue Sun and Maryam Fazel · 2018
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A cubic regularized Newton’s method over Riemannian manifolds
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Adaptive regularization with cubics on manifolds
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Stochastic gradient descent escapes saddle points efficiently
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