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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 7, Pages 1059–1069
DOI: https://doi.org/10.31857/S0044466921070036 (Mi zvmmf11258) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Optimal control

Numerical study of high-dimensional optimization problems using a modification of Polyak's method

A. N. Andrianova, A. S. Anikinb, A. Yu. Gornovb

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia
b Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia
Citations (3)
DOI: https://doi.org/10.31857/S0044466921070036
Abstract: A modification of Polyak’s special method of convex optimization is proposed. The properties of the corresponding algorithm are studied by computational experiments for convex separable and nonseparable optimization problems, nonconvex optimization problems for the potentials of atomic-molecular clusters, and a model optimal control problem. Sequential and parallel versions of the algorithm have been implemented, which made it possible to solve problems with dimensions of up to one hundred billion variables.
Key words: convex optimization, Polyak's method, high-dimensional problems.
Funding agency Grant number
Russian Foundation for Basic Research 18-07-00587
This work was supported by the Russian Foundation for Basic Research, project no. 18-07-00587.
Received: 26.11.2020
Revised: 26.11.2020
Accepted: 11.03.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 7, Pages 1053–1062
DOI: https://doi.org/10.1134/S0965542521070034
Bibliographic databases:
Document Type: Article
UDC: 517.977.5
Language: Russian
Citation: A. N. Andrianov, A. S. Anikin, A. Yu. Gornov, “Numerical study of high-dimensional optimization problems using a modification of Polyak's method”, Zh. Vychisl. Mat. Mat. Fiz., 61:7 (2021), 1059–1069; Comput. Math. Math. Phys., 61:7 (2021), 1053–1062
Citation in format AMSBIB
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\paper Numerical study of high-dimensional optimization problems using a modification of Polyak's method
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\yr 2021
\vol 61
\issue 7
\pages 1059--1069
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\crossref{https://doi.org/10.31857/S0044466921070036}
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\pages 1053--1062
\crossref{https://doi.org/10.1134/S0965542521070034}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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