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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 1, Pages 20–31
DOI: https://doi.org/10.31857/S0044466921010051 (Mi zvmmf11181) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Optimal control

Accelerated meta-algorithm for convex optimization problems

A. V. Gasnikovab, D. M. Dvinskikhabc, P. E. Dvurechenskiibc, D. Kamzolova, V. V. Matyukhina, D. A. Pasechnyuka, N. K. Tupitsaa, A. V. Chernova

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
c Weierstrass institute for Applied Analysis and Stochastics
Citations (13)
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DOI: https://doi.org/10.31857/S0044466921010051
Abstract: An envelope called an accelerated meta-algorithm is proposed. Based on the envelope, accelerated methods for solving convex unconstrained minimization problems in various formulations can be obtained from nonaccelerated versions in a unified manner. Quasi-optimal algorithms for minimizing smooth functions with Lipschitz continuous derivatives of arbitrary order and for solving smooth minimax problems are given as applications. The proposed envelope is more general than existing ones. Moreover, better convergence estimates can be obtained in the case of this envelope and better efficiency can be achieved in practice for a number of problem formulations.
Key words: convex optimization, accelerated proximal method, tensor methods, inexact oracle, sliding, catalyst.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-20005 мол_а_вед
19-31-90170 Аспиранты
18-29-03071 мк
Ministry of Education and Science of the Russian Federation 075-00337-20-03
The work by A. Gasnikov (Section 2) was supported by the Russian Foundation for Basic Research (project no. 18-31-20005 mol_a_ved), Kamzolov’s work (Section 3) was supported by the Russian Foundation for Basic Research (project no. 19-31-90170 Aspiranty), and Dvurechensky’s work (Section 3) was supported by the Russian Foundation for Basic Research (project no. 18-29-03071 mk). Dvinskikh and Matyukhin acknowledge the support of the Ministry of Science and Higher Education of the Russian Federation, state assignment no. 075-00337-20-03, project no. 0714-2020-0005.
Received: 18.04.2020
Revised: 16.06.2020
Accepted: 18.09.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 1, Pages 17–28
DOI: https://doi.org/10.1134/S096554252101005X
Bibliographic databases:
Document Type: Article
UDC: 519.853.62
Language: Russian
Citation: A. V. Gasnikov, D. M. Dvinskikh, P. E. Dvurechenskii, D. Kamzolov, V. V. Matyukhin, D. A. Pasechnyuk, N. K. Tupitsa, A. V. Chernov, “Accelerated meta-algorithm for convex optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 61:1 (2021), 20–31; Comput. Math. Math. Phys., 61:1 (2021), 17–28
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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