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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 1, Pages 52–69
DOI: https://doi.org/10.7868/S0044466918010052 (Mi zvmmf10659) 		 
This article is cited in 42 scientific papers (total in 42 papers)

Universal method for stochastic composite optimization problems

A. V. Gasnikovab, Yu. E. Nesterovcd

a Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, Russia
b Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
c National Research University Higher School of Economics, Moscow, Russia
d Louvain-la-Neuve, Belgium
Citations (42)
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DOI: https://doi.org/10.7868/S0044466918010052
Abstract: A fast gradient method requiring only one projection is proposed for smooth convex optimization problems. The method has a visual geometric interpretation, so it is called the method of similar triangles (MST). Composite, adaptive, and universal versions of MST are suggested. Based on MST, a universal method is proposed for the first time for strongly convex problems (this method is continuous with respect to the strong convexity parameter of the smooth part of the functional). It is shown how the universal version of MST can be applied to stochastic optimization problems.
Key words: fast gradient method, composite optimization, universal method, strongly convex case, stochastic optimization, method of similar triangles.
Funding agency Grant number
Russian Science Foundation 17-11-01027
Russian Foundation for Basic Research 15-31-70001_мол_а_мос
15-31-20571_мол_а_вед
Received: 12.05.2016
Revised: 28.08.2016
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 1, Pages 48–64
DOI: https://doi.org/10.1134/S0965542518010050
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: A. V. Gasnikov, Yu. E. Nesterov, “Universal method for stochastic composite optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 58:1 (2018), 52–69; Comput. Math. Math. Phys., 58:1 (2018), 48–64
Citation in format AMSBIB
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    • This publication is cited in the following 42 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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