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We present a Newton-type method that converges fast from any initialization and for arbitrary convex objectives with Lipschitz Hessians.
A method for the solution of certain non-linear problems in least squares
Kenneth Levenberg · 1944
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Gradient methods of maximization
Jean Bronfenbrenner Crockett and Herman Chernoff · 1955
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An algorithm for least-squares estimation of nonlinear parameters
Donald W. Marquardt · 1963
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Minimization of functions having lipschitz continuous first partial derivatives
Larry Armijo · 1966
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Iterative Solution of Nonlinear Equations in Several Variables
James M. Ortega and Werner C. Rheinboldt · 1970
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A modified Marquardt subroutine for nonlinear least squares
Roger Fletcher · 1971
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The Levenberg-Marquardt algorithm: implementation and theory
Jorge J. Moré · 1978
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The modification of Newton’s method for unconstrained optimization by bounding cubic terms
Andreas Griewank · 1981
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A nonmonotone line search technique for Newton’s method
Luigi Grippo, Francesco Lampariello, and Stephano Luclidi · 1986
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A globally convergent inexact Newton method for systems of monotone equations
Michael V. Solodov and Benav F. Svaiter · 1998
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Trust region methods
Andrew R. Conn, Nicholas I. M. Gould, and Philippe L. Toint · 2000
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On the rate of convergence of the Levenberg-Marquardt method
Nobuo Yamashita and Masao Fukushima · 2001
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Convergence properties of the inexact Levenberg-Marquardt method under local error bound conditions
Hiroshige Dan, Nobuo Yamashita, and Masao Fukushima · 2002
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Convex Optimization
Stephen P. Boyd and Lieven Vandenberghe · 2004
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Regularized Newton methods for convex minimization problems with singular solutions
Dong-Hui Li, Masao Fukushima, Liqun Qi, and Nobuo Yamashita · 2004
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On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
Jin-yan Fan and Ya-xiang Yuan · 2005
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Cubic regularization of Newton method and its global performance
Yurii Nesterov and Boris T. Polyak · 2006
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On the divergence of line search methods
Walter F. Mascarenhas · 2007
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Modified Gauss–Newton scheme with worst case guarantees for global performance
Yurii Nesterov · 2007
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Accelerating the cubic regularization of Newton’s method on convex problems
Yurii Nesterov · 2008
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Estimate sequence methods: extensions and approximations
Michel Baes · 2009
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Regularized Newton method for unconstrained convex optimization
Roman A. Polyak · 2009
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Large-scale machine learning with stochastic gradient descent
Léon Bottou · 2010
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Deep learning via Hessian-free optimization
James Martens · 2010
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A continuous dynamical Newton-like approach to solving monotone inclusions
Hedy Attouch and Benar Fux Svaiter · 2011
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Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
Coralia Cartis, Nicholas I. M. Gould, and Philippe L. Toint · 2011
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How much patience do you have? a worst-case perspective on smooth nonconvex optimization
Coralia Cartis, Nicholas I. M. Gould, and Philippe L. Toint · 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
Coralia Cartis, Nicholas I. M. Gould, and Philippe L. Toint · 2013
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Gradient methods for minimizing composite functions
Yurii Nesterov · 2013
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RSN: Randomized subspace Newton
Robert M. Gower, Dmitry Kovalev, Felix Lieder, and Peter Richtárik · 2019
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SGD: general analysis and improved rates
Robert M. Gower, Nicolas Loizou, Xun Qian, Alibek Sailanbayev, Egor Shulgin, and Peter Richtárik · 2019
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Stochastic Newton and cubic Newton methods with simple local linear-quadratic rates
Dmitry Kovalev, Konstantin Mishchenko, and Peter Richtárik · 2019
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Globally convergent Newton methods for ill-conditioned generalized self-concordant losses
Ulysse Marteau-Ferey, Francis Bach, and Alessandro Rudi · 2019
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Implementable tensor methods in unconstrained convex optimization
Yurii Nesterov · 2019
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Efficient subsampled Gauss-Newton and natural gradient methods for training neural networks
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Introductory lectures on convex optimization: A basic course
Yurii Nesterov · 2013
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Control-limited differential dynamic programming
Yuval Tassa, Nicolas Mansard, and Emo Todorov · 2014
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A regularized Newton method without line search for unconstrained optimization
Kenji Ueda and Nobuo Yamashita · 2014
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Levenberg–Marquardt method for solving systems of absolute value equations
Javed Iqbal, Asif Iqbal, and Muhammad Arif · 2015
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Optimizing neural networks with Kronecker-factored approximate curvature
James Martens and Roger Grosse · 2015
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A dynamic approach to a proximal-Newton method for monotone inclusions in Hilbert spaces, with complexity O ( 1 / n 2 ) O(1/n^{2})
Hedy Attouch, Maicon Marques Alves, and Benar Fux Svaiter · 2016
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Simple examples for the failure of Newton’s method with line search for strictly convex minimization
Florian Jarre and Philippe L. Toint · 2016
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Yi Ren and Donald Goldfarb · 2019
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Wireless networks design in the era of deep learning: Model-based, AI-based, or both?
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Convergence and complexity analysis of a levenberg–marquardt algorithm for inverse problems
El Houcine Bergou, Youssef Diouane, and Vyacheslav Kungurtsev · 2020
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DINO: Distributed Newton-type optimization method
Rixon Crane and Fred Roosta · 2020
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Inexact tensor methods with dynamic accuracies
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Practical quasi-Newton methods for training deep neural networks
Donald Goldfarb, Yi Ren, and Achraf Bahamou · 2020
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Stochastic subspace cubic Newton method
Filip Hanzely, Nikita Doikov, Peter Richtárik, and Yurii Nesterov · 2020
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Practical reinforcement learning for MPC: Learning from sparse objectives in under an hour on a real robot
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Adaptive gradient descent without descent
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Constrained Levenberg-Marquardt method with global complexity bound
Naoki Marumo, Takayuki Okuno, and Akiko Takeda · 2020
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Random Reshuffling: Simple analysis with vast improvements
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Inexact accelerated high-order proximal-point methods
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Superfast second-order methods for unconstrained convex optimization
Yurii Nesterov · 2020
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DAve-QN: A distributed averaged quasi-Newton method with local superlinear convergence rate
Saeed Soori, Konstantin Mishchenko, Aryan Mokhtari, Maryam Mehri Dehnavi, and Mert Gürbüzbalaban · 2020
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Curiosities and counterexamples in smooth convex optimization
Jérôme Bolte and Edouard Pauwels · 2021
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Optimization methods for fully composite problems
Nikita Doikov and Yurii Nesterov · 2021
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Greedy quasi-newton methods with explicit superlinear convergence
Anton Rodomanov and Yurii Nesterov · 2021
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Super-universal regularized Newton method
Nikita Doikov, Konstantin Mishchenko, and Yurii Nesterov · 2022
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