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Trust region and cubic regularization methods have demonstrated good performance in small scale non-convex optimization, showing the ability to escape from saddle points.
Updating quasi-newton matrices with limited storage
Jorge Nocedal · 1980
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Estimating the largest eigenvalue by the power and lanczos algorithms with a random start
Jacek Kuczyński and Henryk Woźniakowski · 1992
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Trust region methods
Andrew R Conn, Nicholas IM Gould, and Ph L Toint · 2000
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Solving large scale linear prediction problems using stochastic gradient descent algorithms
Tong Zhang · 2004
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Fast monte carlo algorithms for matrices i: Approximating matrix multiplication
Petros Drineas, Ravi Kannan, and Michael W Mahoney · 2006
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Cubic regularization of newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
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Jorge Nocedal and Stephen Wright · 2006
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Note on sampling without replacing from a finite collection of matrices
David Gross and Vincent Nesme · 2010
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Adaptive cubic regularisation methods for unconstrained optimization. part i: motivation, convergence and numerical results
Coralia Cartis, Nicholas IM Gould, and Philippe L Toint · 2011
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Adaptive cubic regularisation methods for unconstrained optimization. part ii: worst-case function-and derivative-evaluation complexity
Coralia Cartis, Nicholas IM Gould, and Philippe L Toint · 2011
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Pegasos: Primal estimated sub-gradient solver for svm
Shai Shalev-Shwartz, Yoram Singer, Nathan Srebro, and Andrew Cotter · 2011
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On the use of stochastic hessian information in optimization methods for machine learning
Richard H Byrd, Gillian M Chin, Will Neveitt, and Jorge Nocedal · 2011
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Randomized algorithms for matrices and data
Michael W Mahoney · 2011
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A probabilistic and ripless theory of compressed sensing
Emmanuel J Candes and Yaniv Plan · 2011
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Recovering low-rank matrices from few coefficients in any basis
David Gross · 2011
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Accelerating stochastic gradient descent using predictive variance reduction
Rie Johnson and Tong Zhang · 2013
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Saga: A fast incremental gradient method with support for non-strongly convex composite objectives
Aaron Defazio, Francis Bach, and Simon Lacoste-Julien · 2014
Sub-sampled newton methods i: globally convergent algorithms
Farbod Roosta-Khorasani and Michael W Mahoney · 2016
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Sub-sampled newton methods ii: Local convergence rates
Farbod Roosta-Khorasani and Michael W Mahoney · 2016
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Faster eigenvector computation via shift-and-invert preconditioning
Dan Garber, Elad Hazan, Chi Jin, Sham M Kakade, Cameron Musco, Praneeth Netrapalli, and Aaron Sidford · 2016
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No spurious local minima in nonconvex low rank problems: A unified geometric analysis
Rong Ge, Chi Jin, and Yi Zheng · 2017
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Convergence rates of sub-sampled newton methods
Murat A Erdogdu and Andrea Montanari · 2015
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Accelerated gradient methods for nonconvex nonlinear and stochastic programming
Saeed Ghadimi and Guanghui Lan · 2016
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Stochastic variance reduction for nonconvex optimization
Sashank J Reddi, Ahmed Hefny, Suvrit Sra, Barnabas Poczos, and Alex Smola · 2016
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Variance reduction for faster non-convex optimization
Zeyuan Allen-Zhu and Elad Hazan · 2016
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Efficient approaches for escaping higher order saddle points in non-convex optimization
Animashree Anandkumar and Rong Ge · 2016
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Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M Kakade, and Michael I Jordan · 2017
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Newton-type methods for non-convex optimization under inexact hessian information
Peng Xu, Farbod Roosta-Khorasani, and Michael W Mahoney · 2017
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Second-order optimization for non-convex machine learning: An empirical study
Peng Xu, Farbod Roosta-Khorasan, and Michael W Mahoney · 2017
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Sub-sampled cubic regularization for non-convex optimization
Jonas Moritz Kohler and Aurelien Lucchi · 2017
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Stochastic cubic regularization for fast nonconvex optimization
Nilesh Tripuraneni, Mitchell Stern, Chi Jin, Jeffrey Regier, and Michael I Jordan · 2017
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Accelerated methods for nonconvex optimization
Yair Carmon, John C Duchi, Oliver Hinder, and Aaron Sidford · 2018
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