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We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems.
A method for the solution of certain non-linear problems in least squares
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Functional analysis and applied mathematics. [in Russian]
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An algorithm for least-squares estimation of nonlinear parameters
Donald W. Marquardt · 1963
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Maximization by quadratic hill-climbing
Stephen M. Goldfeld, Richard E. Quandt, and Hale F. Trotter · 1966
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Interior-point polynomial algorithms in convex programming
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Trust region methods
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Iterative solution of nonlinear equations in several variables
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Cubic regularization of Newton’s method and its global performance
Yurii Nesterov and Boris Polyak · 2006
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Boris Polyak · 2007
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Accelerating the cubic regularization of Newton’s method on convex problems
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Estimate sequence methods: extensions and approximations
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Regularized Newton method for unconstrained convex optimization
Roman Polyak · 2009
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Kenji Ueda and Nobuo Yamashita · 2009
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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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Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function-and derivative-evaluation complexity
Coralia Cartis, Nicholas I. M. Gould, and Philippe L. Toint · 2011
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An accelerated hybrid proximal extragradient method for convex optimization and its implications to second-order methods
Renato D. C. Monteiro and Benar F. Svaiter · 2013
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A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications
Heinz H. Bauschke, Jérôme Bolte, and Marc Teboulle · 2016
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A superlinearly-convergent proximal Newton-type method for the optimization of finite sums
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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
Ernesto G. Birgin, J. L. Gardenghi, José Mario Martínez, Sandra Augusta Santos, and Philippe L. Toint · 2017
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Regularized Newton methods for minimizing functions with Hölder continuous Hessians
Geovani N. Grapiglia and Yurii Nesterov · 2017
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Contracting proximal methods for smooth convex optimization
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Tensor methods for minimizing convex functions with Hölder continuous higher-order derivatives
Geovani N. Grapiglia and Yurii Nesterov · 2020
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Stochastic subspace cubic Newton method
Filip Hanzely, Nikita Doikov, Peter Richtárik, and Yurii Nesterov · 2020
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Near-optimal hyperfast second-order method for convex optimization and its sliding
Dmitry Kamzolov and Alexander Gasnikov · 2020
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New second-order and tensor methods in Convex Optimization
Nikita Doikov · 2021
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Gradient regularization of Newton method with Bregman distances
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Local convergence of tensor methods
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Minimizing uniformly convex functions by cubic regularization of Newton method
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Regularized Newton method with global O ( 1 / k 2 ) {O}(1/k^{2}) convergence
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