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A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed.
The modification of Newton’s method for unconstrained optimization by bounding cubic terms
A. Griewank · 1981
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Black-box complexity of local minimization
S. A. Vavasis · 1993
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Trust-Region Methods
A. R. Conn, N. I. M. Gould, and Ph. L. Toint · 2000
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Introductory Lectures on Convex Optimization
Yu. Nesterov · 2004
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Cubic regularization of Newton method and its global performance
Yu. Nesterov and B. T. Polyak · 2006
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Recursive trust-region methods for multiscale nonlinear optimization
S. Gratton, A. Sartenaer, and Ph. L. Toint · 2008
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Trust-region and other regularization of linear least-squares problems
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2009
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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 oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2012
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Convergence of trust-region methods based on probabilistic models
A. Bandeira, K. Scheinberg and L. Vicente · 2014
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Simple unified convergence proofs for the trust-region and a new ARC variant
J. P. Dussault · 2015
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An Introduction to Matrix Concentration Inequalities
J. Tropp · 2015
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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, and Ph. L. Toint · 2017
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Stochastic cubic regularization for fast nonconvex optimization
N. Tripuraneni, M. Stern, J. Regier, and M. I. Jordan · 2017
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Newton-type methods for non-convex optimization under inexact Hessian information
P. Xu, F. Roosta-Khorasani, and M. W. Mahoney · 2017
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Optimization Methods for Large-Scale Machine Learning
L. Bottou, F. E. Curtis and J. Nocedal · 2018
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C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2018
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Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2018
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Global convergence rate analysis of unconstrained optimization methods based on probabilistic models
C. Cartis and K. Scheinberg · 2018
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On adaptive cubic regularization Newton’s methods for convex optimization via random sampling
X. Chen, B. Jiang, T. Lin, and S. Zhang · 2018
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Minimizing convex quadratics with variable precision Krylov methods
S. Gratton, E. Simon, and Ph. L. Toint · 2018
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Convergence rate analysis of a stochastic trust region method via supermartingales
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