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In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems.
The extragradient method for finding saddle points and other problems
Korpelevich, G. M. (1976) · 1976
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Problem complexity and method efficiency in optimization
Nemirovskij, A. S. and Yudin, D. B. (1983) · 1983
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A method for solving the convex programming problem with convergence rate o (1/kˆ 2)
Nesterov, Y. E. (1983) · 1983
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Introductory lectures on convex optimization: A basic course
Nesterov, Y. (2003) · 2003
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Cubic regularization of newton method and its global performance
Nesterov, Y. and Polyak, B. T. (2006) · 2006
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Accelerating the cubic regularization of newton’s method on convex problems
Nesterov, Y. (2008) · 2008
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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) · 2013
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Lower bounds for higher-order convex optimization
Agarwal, N. and Hazan, E. (2018) · 2018
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Optimal tensor methods in smooth convex and uniformly convexoptimization
Gasnikov, A., Dvurechensky, P., Gorbunov, E., Vorontsova, E., Selikhanovych, D., and Uribe, C. A. (2019a)
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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. (2019b)
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Implementable tensor methods in unconstrained convex optimization
Nesterov, Y. (2021a)
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Inexact high-order proximal-point methods with auxiliary search procedure
Nesterov, Y. (2021b)
Cited in the paper.
Oracle complexity of second-order methods for smooth convex optimization
Arjevani, Y., Shamir, O., and Shiff, R. (2019) · 2019
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Near-optimal method for highly smooth convex optimization
Bubeck, S., Jiang, Q., Lee, Y. T., Li, Y., and Sidford, A. (2019) · 2019
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An optimal high-order tensor method for convex optimization
Jiang, B., Wang, H., and Zhang, S. (2019) · 2019
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