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We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving and generalizing the results of Cartis, Gould and Toint (2010,2011).
Maximization by quadratic hill-climbing
S. M. Goldfeldt, R. E. Quandt, and H. F. Trotter · 1966
Earlier work this paper cites.
The modification of Newton’s method for unconstrained optimization by bounding cubic terms
A. Griewank · 1981
Earlier work this paper cites.
Black-box complexity of local minimization
S. A. Vavasis · 1993
Earlier work this paper cites.
Numerical Methods for Unconstrained Optimization and Nonlinear Equations
J. E. Dennis and R. B. Schnabel · 1996
Earlier work this paper cites.
A linesearch algorithm with memory for unconstrained optimization
N. I. M. Gould, S. Lucidi, M. Roma, and Ph. L. Toint · 1998
Earlier work this paper cites.
Numerical Optimization
J. Nocedal and S. J. Wright · 1999
Earlier work this paper cites.
Trust-Region Methods
A. R. Conn, N. I. M. Gould, and Ph. L. Toint · 2000
Earlier work this paper cites.
Introductory Lectures on Convex Optimization
Yu. Nesterov · 2004
Earlier work this paper cites.
Cubic regularization of Newton method and its global performance
Yu. Nesterov and B. T. Polyak · 2006
Earlier work this paper cites.
Affine conjugate adaptive Newton methods for nonlinear elastomechanics
M. Weiser, P. Deuflhard, and B. Erdmann · 2007
Earlier work this paper cites.
Recursive trust-region methods for multiscale nonlinear optimization
S. Gratton, A. Sartenaer, and Ph. L. Toint · 2008
Earlier work this paper cites.
On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization
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Earlier work this paper cites.
Convergence properties of the regularized Newton method for the unconstrained nonconvex optimization
K. Ueda and N. Yamashita · 2010
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On a global complexity bound of the Levenberg-Marquardt method
K. Ueda and N. Yamashita · 2010
Earlier work this paper cites.
Adaptive cubic overestimation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
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Adaptive cubic overestimation methods for unconstrained optimization. Part II: worst-case function-evaluation complexity
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2011
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On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
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Optimal Newton-type methods for nonconvex optimization
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2011
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A note on the complexity of
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An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2012
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Complexity bounds for second-order optimality in unconstrained optimization
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2012
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On the complexity of the steepest-descent with exact linesearches
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Updating the regularization parameter in the adaptive cubic regularization algorithm
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A trust-region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization
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Worst-case complexity of smoothing quadratic regularization methods for non-Lipschitzian optimization
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On the complexity of finding first-order critical points in constrained nonlinear optimization
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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
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K. Scheinberg and X. Tang · 2016
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