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We consider the problem of finding an approximate second-order stationary point of a constrained non-convex optimization problem.
The modification of newton’s method for unconstrained optimization by bounding cubic terms
A. Griewank · 1981
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Some np-complete problems in quadratic and nonlinear programming
K. G. Murty and S. N. Kabadi · 1987
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Nonlinear programming
D. P. Bertsekas · 1999
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Trust region methods
A. R. Conn, N. I. Gould, and P. L. Toint · 2000
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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. 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. Gould, and P. L. Toint · 2011
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An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
C. Cartis, N. Gould, and P. L. Toint · 2012
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A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization
S. Lu, Z. Wei, and L. Li · 2012
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On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization
C. Cartis, N. I. Gould, and P. L. Toint · 2013
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Y. Hsia and R.-L. Sheu · 2013
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Introductory lectures on convex optimization: A basic course
Y. Nesterov · 2013
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On the computational complexity of membership problems for the completely positive cone and its dual
P. J. Dickinson and L. Gijben · 2014
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On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods
C. Cartis, N. I. Gould, and P. L. Toint · 2015
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Escaping from saddle points—online stochastic gradient for tensor decomposition
R. Ge, F. Huang, C. Jin, and Y. Yuan · 2015
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When are nonconvex problems not scary?
J. Sun, Q. Qu, and J. Wright · 2015
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Efficient approaches for escaping higher order saddle points in non-convex optimization
A. Anandkumar and R. Ge · 2016
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On the low-rank approach for semidefinite programs arising in synchronization and community detection
A. S. Bandeira, N. Boumal, and V. Voroninski · 2016
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Nonconvex phase synchronization
N. Boumal · 2016
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Matrix completion has no spurious local minimum
R. Ge, J. D. Lee, and T. Ma · 2016
A trust region algorithm with a worst-case iteration complexity of o( ϵ − 3 / 2 \epsilon^{-3/2} ) for nonconvex optimization
F. E. Curtis, D. P. Robinson, and M. Samadi · 2017
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Gradient descent can take exponential time to escape saddle points
S. S. Du, C. Jin, J. D. Lee, M. I. Jordan, A. Singh, and B. Poczos · 2017
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How to escape saddle points efficiently
C. Jin, R. Ge, P. Netrapalli, S. M. Kakade, and M. 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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Depth creates no bad local minima
H. Lu and K. Kawaguchi · 2017
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Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
S. Ghadimi, G. Lan, and H. Zhang · 2016
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Deep learning without poor local minima
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Gradient descent converges to minimizers
J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht · 2016
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A geometric analysis of phase retrieval
J. Sun, Q. Qu, and J. Wright · 2016
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Second-order optimality and beyond: Characterization and evaluation complexity in convexly constrained nonlinear optimization
C. Cartis, N. I. Gould, and P. L. Toint · 2017
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Complete dictionary recovery over the sphere i: Overview and the geometric picture
J. Sun, Q. Qu, and J. Wright · 2017
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Complete dictionary recovery over the sphere ii: Recovery by riemannian trust-region method
J. Sun, Q. Qu, and J. Wright · 2017
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On the behavior of the expectation-maximization algorithm for mixture models
B. Barazandeh and M. Razaviyayn · 2018
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M. Hong, J. D. Lee, and M. Razaviyayn · 2018
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Escaping saddle points in constrained optimization
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Learning deep models: Critical points and local openness
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Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization
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