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Motivated by TRACE algorithm [Curtis et al.
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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On the complexity of finding first-order critical points in constrained nonlinear optimization
C. Cartis, N. I. Gould, and P. L. Toint · 2014
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Complexity analysis of interior point algorithms for non-lipschitz and nonconvex minimization
W. Bian, X. Chen, and Y. Ye · 2015
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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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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
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Gradient descent converges to minimizers
J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht · 2016
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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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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On regularization and active-set methods with complexity for constrained optimization
E. Birgin and J. Martínez · 2018
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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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Exploiting negative curvature in deterministic and stochastic optimization
F. E. Curtis and D. P. Robinson · 2017
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F. E. Curtis, D. P. Robinson, and M. Samadi · 2017
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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
Cited alongside, same era.
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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M. Hong, J. D. Lee, and M. Razaviyayn · 2018
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Escaping saddle points in constrained optimization
A. Mokhtari, A. Ozdaglar, and A. Jadbabaie · 2018
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Convergence to second-order stationarity for constrained non-convex optimization
M. Nouiehed, J. D. Lee, and M. Razaviyayn · 2018
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Learning deep models: Critical points and local openness
M. Nouiehed and M. Razaviyayn · 2018
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Finding second-order stationary solutions using a perturbed projected gradient descent algorithm for non-convex linearly constrained problems
S. Lu, M. Razaviyayn, B. Yang, K. Huang, and M. Hong · 2019
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Solving a class of non-convex min-max games using iterative first order methods
M. Nouiehed, M. Sanjabi, J. D. Lee, and M. Razaviyayn · 2019
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A log-barrier newton-cg method for bound constrained optimization with complexity guarantees
M. O’Neill and S. J. Wright · 2019
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