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In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective.
Tensor methods for minimizing functions with Hölder continuous higher-order derivatives
Grapiglia, G. N. and Nesterov, Y · 1904
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Minimizing uniformly convex functions by cubic regularization of Newton method
Doikov, N. and Nesterov, Y · 1905
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On inexact solution of auxiliary problems in tensor methods for convex optimization
Grapiglia, G. N. and Nesterov, Y · 1907
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Tensor methods for finding approximate stationary points of convex functions
Grapiglia, G. N. and Nesterov, Y · 1907
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A method for solving the convex programming problem with convergence rate O(1/kˆ2)
Nesterov, Y · 1983
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New proximal point algorithms for convex minimization
Güler, O · 1992
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Interior-point polynomial algorithms in convex programming
Nesterov, Y. and Nemirovskii, A · 1994
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Cubic regularization of Newton’s method and its global performance
Nesterov, Y. and Polyak, B. T · 2006
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Numerical optimization 2nd, 2006
Nocedal, J. and Wright, S. J · 2006
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Accelerating the cubic regularization of Newton’s method on convex problems
Nesterov, Y · 2008
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Estimate sequence methods: extensions and approximations
Baes, M · 2009
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On solving trust-region and other regularised subproblems in optimization
Gould, N. I., Robinson, D. P., and Thorne, H. S · 2010
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Convergence rates of inexact proximal-gradient methods for convex optimization
Schmidt, M., Roux, N. L., and Bach, F. R · 2011
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An accelerated hybrid proximal extragradient method for convex optimization and its implications to second-order methods
Monteiro, R. D. and Svaiter, B. F · 2013
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Gradient methods for minimizing composite functions
Nesterov, Y · 2013
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A universal catalyst for first-order optimization
Lin, H., Mairal, J., and Harchaoui, Z · 2015
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A descent lemma beyond lipschitz gradient continuity: first-order methods revisited and applications
Bauschke, H. H., Bolte, J., and Teboulle, M · 2016
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Finding approximate local minima faster than gradient descent
Agarwal, N., Allen-Zhu, Z., Bullins, B., Hazan, E., and Ma, T · 2017
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First-order methods in optimization , volume 25
Beck, A · 2017
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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
Birgin, E. G., Gardenghi, J., Martínez, J. M., Santos, S. A., and Toint, P. L · 2017
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Sub-sampled cubic regularization for non-convex optimization
Kohler, J. M. and Lucchi, A · 2017
Stochastic variance-reduced cubic regularization for nonconvex optimization
Wang, Z., Zhou, Y., Liang, Y., and Lan, G · 2018
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Oracle complexity of second-order methods for smooth convex optimization
Arjevani, Y., Shamir, O., and Shiff, R · 2019
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Gradient descent finds the cubic-regularized nonconvex Newton step
Carmon, Y. and Duchi, J · 2019
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Universal regularization methods: varying the power, the smoothness and the accuracy
Cartis, C., Gould, N. I., and Toint, P. L · 2019
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Contracting proximal methods for smooth convex optimization
Doikov, N. and Nesterov, Y · 2019
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Local convergence of tensor methods
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Forward-backward splitting with bregman distances
Van Nguyen, Q · 2017
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Fast minimization of structured convex quartics
Bullins, B · 2018
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Global convergence rate analysis of unconstrained optimization methods based on probabilistic models
Cartis, C. and Scheinberg, K · 2018
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Randomized block cubic Newton method
Doikov, N. and Richtárik, P · 2018
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A unified adaptive tensor approximation scheme to accelerate composite convex optimization
Jiang, B., Lin, T., and Zhang, S · 2018
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Catalyst acceleration for first-order convex optimization: from theory to practice
Lin, H., Mairal, J., and Harchaoui, Z · 2018
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Doikov, N. and Nesterov, Y · 2019
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Near optimal methods for minimizing convex functions with lipschitz p p -th derivatives
Gasnikov, A., Dvurechensky, P., Gorbunov, E., Vorontsova, E., Selikhanovych, D., Uribe, C. A., Jiang, B., Wang, H., Zhang, S., Bubeck, S., et al · 2019
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Adaptive catalyst for smooth convex optimization
Ivanova, A., Grishchenko, D., Gasnikov, A., and Shulgin, E · 2019
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A generic acceleration framework for stochastic composite optimization
Kulunchakov, A. and Mairal, J · 2019
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A stochastic tensor method for non-convex optimization
Lucchi, A. and Kohler, J · 2019
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Inexact basic tensor methods
Nesterov, Y · 2019
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Smoothness parameter of power of euclidean norm
Rodomanov, A. and Nesterov, Y · 2019
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Towards unified acceleration of high-order algorithms under Hölder continuity and uniform convexity
Song, C. and Ma, Y · 2019
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Stochastic variance-reduced cubic regularization methods
Zhou, D., Xu, P., and Gu, Q · 2019
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