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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 5, Pages 889–894
DOI: https://doi.org/10.1134/S0044466919050077 (Mi zvmmf10900) 		 
This article is cited in 12 scientific papers (total in 12 papers)

An adaptive proximal method for variational inequalities

A. V. Gasnikovabc, P. E. Dvurechenskiicd, F. S. Stonyakinae, A. A. Titova

a Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia
b State University—Higher School of Economics, Moscow, 125319 Russia
c Kharkevich Institute for Information Transmission Problems, Moscow, 127051 Russia
d Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 10117 Germany
e Crimea Federal University, Simferopol, 295007 Russia
Citations (12)
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DOI: https://doi.org/10.1134/S0044466919050077
Abstract: A novel analog of Nemirovski's proximal mirror method with an adaptive choice of constants in the minimized prox-mappings at each iteration for variational inequalities with a Lipschitz continuous field is proposed. Estimates of the number of iterations needed to attain the desired quality of solution of the variational inequality are obtained. It is shown how the proposed approach can be extended for the case of Hölder continuous field. A modification of the proposed algorithm for the case of an inexact oracle for the field operator is also considered.
Key words: variational inequality, proximal method, adaptive method, Hölder continuous field operator, inexact oracle.
Funding agency Grant number
Russian Science Foundation 18-71-00048
Ministry of Education and Science of the Russian Federation МД-1320.2018.1
Russian Foundation for Basic Research 18-29-03071_мк
18-31-20005_мол_а_вед
The work by F.S. Stonyakin on the proof of Theorem 2, Algorithm 1, and Remark 3 was supported by the Russian Science Foundation, project no. 18-71-00048. The work by A.V. Gasnikov on Algorithm 2 and the proof of Theorem 3 was supported by the President of the Russian Federation, project no. MD-1320.2018.1 for young Russian doctors of science, and by the Top 100 Program 5 of the State University--Higher School of Economics. The work by P.E. Dvurechensky on Algorithm 2 and the proof of Theorem 3 was supported by the Russian Foundation for Basic Research, project nos. 18-29-03071_mk and 18-31-20005 mol_a_ved.
Received: 11.12.2017
Revised: 19.12.2018
Accepted: 19.12.2018
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 5, Pages 836–841
DOI: https://doi.org/10.1134/S0965542519050075
Bibliographic databases:
Document Type: Article
UDC: 519.217
Language: Russian
Citation: A. V. Gasnikov, P. E. Dvurechenskii, F. S. Stonyakin, A. A. Titov, “An adaptive proximal method for variational inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 889–894; Comput. Math. Math. Phys., 59:5 (2019), 836–841
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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