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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 2, Pages 189–217
DOI: https://doi.org/10.31857/S0044466923020059
(Mi zvmmf11507)
 

This article is cited in 2 scientific papers (total in 2 papers)

General numerical methods

A unified analysis of variational inequality methods: variance reduction, sampling, quantization, and coordinate descent

A. N. Beznosikova, A. V. Gasnikovabc, K. E. Zainullinaa, A. Yu. Maslovskiia, D. A. Pasechnyukab

a Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia
b Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, 127051, Moscow, Russia
c Caucasus Mathematical Center, Adyghe State University, 385000, Maykop, Republic of Adygea, Russia
Citations (2)
Abstract: We present a unified analysis of methods for such a wide class of problems as variational inequalities, which include minimization and saddle point problems as special cases. The analysis is developed relying on the extragradient method, which is a classic technique for solving variational inequalities. We consider the monotone and strongly monotone cases, which correspond to convex-concave and strongly-convex-strongly-concave saddle point problems. The theoretical analysis is based on parametric assumptions about extragradient iterations. Therefore, it can serve as a strong basis for combining existing methods of various types and for creating new algorithms. Specifically, to show this, we develop new robust methods, including methods with quantization, coordinate methods, and distributed randomized local methods. Most of these approaches have never been considered in the generality of variational inequalities and have previously been used only for minimization problems. The robustness of the new methods is confirmed by numerical experiments with GANs.
Key words: extragradient method, stochastic variational inequalities, quantization, variance reduction.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-00337-20-03
This work was supported by the Ministry of Science and Higher Education of the Russian Federation, state assignment no. 075-00337-20-03, project no. 0714-2020-0005.
Received: 28.01.2022
Revised: 28.01.2022
Accepted: 14.10.2022
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 2, Pages 147–174
DOI: https://doi.org/10.1134/S0965542523020045
Bibliographic databases:
Document Type: Article
UDC: 519.85
Language: Russian
Citation: A. N. Beznosikov, A. V. Gasnikov, K. E. Zainullina, A. Yu. Maslovskii, D. A. Pasechnyuk, “A unified analysis of variational inequality methods: variance reduction, sampling, quantization, and coordinate descent”, Zh. Vychisl. Mat. Mat. Fiz., 63:2 (2023), 189–217; Comput. Math. Math. Phys., 63:2 (2023), 147–174
Citation in format AMSBIB
\Bibitem{BezGasZai23}
\by A.~N.~Beznosikov, A.~V.~Gasnikov, K.~E.~Zainullina, A.~Yu.~Maslovskii, D.~A.~Pasechnyuk
\paper A unified analysis of variational inequality methods: variance reduction, sampling, quantization, and coordinate descent
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 2
\pages 189--217
\mathnet{http://mi.mathnet.ru/zvmmf11507}
\crossref{https://doi.org/10.31857/S0044466923020059}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4573226}
\elib{https://elibrary.ru/item.asp?id=50435447}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 2
\pages 147--174
\crossref{https://doi.org/10.1134/S0965542523020045}
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  • https://www.mathnet.ru/eng/zvmmf/v63/i2/p189
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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