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The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for non-convex optimization because of its capability of finding an approximate local solution with second-order guarantee.
Fast exact multiplication by the Hessian
B. A. Pearlmutter · 1994
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Introductory Lectures on Convex Optimization: A Basic Course
Y. Nesterov · 2004
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Cubic regularization of newton method and its global performance
Y. Nesterov and B. T. Polyak · 2006
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Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
C. Cartis, N. I. M. Gould, and P. L. Toint · 2011
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Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function-and derivative-evaluation complexity
C. Cartis, N. I. M. Gould, and P. L. Toint · 2011
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Accelerating stochastic gradient descent using predictive variance reduction
R. Johnson and T. Zhang · 2013
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Linear convergence with condition number independent access of full gradients
L. Zhang, M. Mahdavi, and R. Jin · 2013
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A proximal stochastic gradient method with progressive variance reduction
L. Xiao and T. Zhang · 2014
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On the use of iterative methods in cubic regularization for unconstrained optimization
T. Bianconcini, G. Liuzzi, B. Morini, and M. Sciandrone · 2015
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Convergence rates of sub-sampled Newton methods
M. A. Erdogdu and A. Montanari · 2015
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An introduction to matrix concentration inequalities
J. A. Tropp · 2015
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Variance reduction for faster non-convex optimization
Z. Allen-Zhu and E. Hazan · 2016
Cited alongside, same era.
Gradient descent efficiently finds the cubic-regularized non-convex Newton step
Y. Carmon and J. C. Duchi · 2016
Cited alongside, same era.
A linear-time algorithm for trust region problems
E. Hazan and T. Koren · 2016
Cited alongside, same era.
Stochastic variance reduction for nonconvex optimization
S. Reddi, A. Hefny, S. Sra, B. Póczós, and A. Smola · 2016
Cited alongside, same era.
Sub-sampled cubic regularization for non-convex optimization
J. M. Kohler and A. Lucchi · 2017
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Stochastic cubic regularization for fast nonconvex optimization
N. Tripuraneni, M. Stern, C. Jin, J. Regier, and M. I. Jordan · 2017
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Approximate Newton methods and their local convergence
H. Ye, L. Luo, and Z. Zhang · 2017
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On adaptive cubic regularized Newton’s methods for convex optimization via random sampling
X. Chen, B. Jiang, T. Lin, and S. Zhang · 2018
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A generic approach for escaping saddle points
S. Reddi, M. Zaheer, S. Sra, B. Póczós, F. Bach, R. Salakhutdinov, and A. Smola · 2018
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Sub-sampled Newton methods I: Globally convergent algorithms
F. Roosta-Khorasani and M. W. Mahoney · 2016
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Sub-sampled Newton methods with non-uniform sampling
P. Xu, J. Yang, F. Roosta-Khorasani, C. Ré, and M. W. Mahoney · 2016
Cited alongside, same era.
Finding approximate local minima faster than gradient descent
N. Agarwal, Z. Allen-Zhu, B. Bullins, E. Hazan, and T. Ma · 2017
Cited alongside, same era.
A note on inexact condition for cubic regularized Newton’s method
Z. Wang, Y. Zhou, Y. Liang, and G. Lan · 2018
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Sample complexity of stochastic variance-reduced cubic regularization for nonconvex optimization
Z. Wang, Y. Zhou, Y. Liang, and G. Lan · 2018
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Newton-type methods for non-convex optimization under inexact Hessian information
P. Xu, F. Roosta-Khorasani, and M. W. Mahoney · 2018
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Stochastic variance-reduced cubic regularized Newton methods
D. Zhou, P. Xu, and Q. Gu · 2018
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