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This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature.
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
Cornelius Lanczos · 1950
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On the use of directions of negative curvature in a modified newton method
Jorge J Moré and Danny C Sorensen · 1979
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Curvilinear path steplength algorithms for minimization which use directions of negative curvature
Donald Goldfarb · 1980
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Computing modified newton directions using a partial cholesky factorization
Anders Forsgren, Philip E Gill, and Walter Murray · 1995
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Exploiting negative curvature directions in linesearch methods for unconstrained optimization
N. I. M. Gould, S. Lucidi, M. Roma, and PH. L. Toint · 2000
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A Box-Constrained Optimization Algorithm with Negative Curvature Directions and Spectral Projected Gradients
E. G. Birgin and J. M. Martínez · 2001
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Numerical Optimization
J. Nocedal and S. J. Wright · 2006
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Sparse subspace clustering
Ehsan Elhamifar and René Vidal · 2009
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Deep learning via hessian-free optimization
James Martens · 2010
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Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
Yann N Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, and Yoshua Bengio · 2014
Cited alongside, same era.
Equilibrated adaptive learning rates for non-convex optimization
Yann Dauphin, Harm de Vries, and Yoshua Bengio · 2015
Cited alongside, same era.
Escaping From Saddle Points — Online Stochastic Gradient for Tensor Decomposition
R. Ge, F. Huang, C. Jin, and Y. Yuan · 2015
Cited alongside, same era.
Cutest: a constrained and unconstrained testing environment with safe threads for mathematical optimization
Nicholas IM Gould, Dominique Orban, and Philippe L Toint · 2015
Cited alongside, same era.
A solver for nonconvex bound-constrained quadratic optimization
Hassan Mohy-ud-Din and Daniel P. Robinson · 2015
Cited alongside, same era.
On large-batch training for deep learning: Generalization gap and sharp minima
Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Peter Tang · 2016
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Gradient descent only converges to minimizers
Jason D. Lee, Max Simchowitz, Michael I. Jordan, and Benjamin Recht · 2016
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A nonconvex formulation for low rank subspace clustering: Algorithms and convergence analysis
Hao Jiang, Daniel P. Robinson, and René Vidal · 2017
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How to escape saddle points efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M Kakade, and Michael I Jordan · 2017
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First-order methods almost always avoid saddle points
J. D. Lee, I. Panageas, G. Piliouras, M. Simchowitz, M. I. Jordan, and B. Recht · 2017
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A. Neelakantan, L. Vilnis, Q. V. Le, I. Sutskever, L. Kaiser, K. Kurach, and J. Martens · 2015
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Optimization Methods for Large-Scale Machine Learning
L. Bottou, F. E. Curtis, and J. Nocedal · 2016
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A stabilized SQP method: global convergence
Philip E Gill, Vyacheslav Kungurtsev, and Daniel P Robinson · 2016
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A stabilized SQP method: superlinear convergence
Philip E. Gill, Vyacheslav Kungurtsev, and Daniel P. Robinson · 2016
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Gradient-based learning applied to document recognition
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner
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Mingrui Liu and Tianbao Yang · 2017
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A Second Order Method for Nonconvex Optimization
S. Paternain, A. Mokhtari, and A. Ribeiro · 2017
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Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization
Clément W Royer and Stephen J Wright · 2017
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