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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 7, Pages 1137–1150
DOI: https://doi.org/10.1134/S0044466919070081 (Mi zvmmf10921) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Fast gradient descent for convex minimization problems with an oracle producing a (δ,L)-model of function at the requested point

A. V. Gasnikovabc, A. I. Turina

a State University – Higher School of Economics, Moscow, 125319 Russia
b Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia
c Kharkevich Institute for Information Transmission Problems, Moscow, 127051 Russia
Citations (17)
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DOI: https://doi.org/10.1134/S0044466919070081
Abstract: A new concept of (δ,L) -model of a function that is a generalization of the Devolder–Glineur–Nesterov (δ,L)-oracle is proposed. Within this concept, the gradient descent and fast gradient descent methods are constructed and it is shown that constructs of many known methods (composite methods, level methods, conditional gradient and proximal methods) are particular cases of the methods proposed in this paper.
Key words: gradient descent, fast gradient descent, model of function, universal method, conditional gradient method, composite optimization.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 18-31-20005_мол_а_вед
Russian Science Foundation 17-11-01027
The work by Tyurin was supported by the program of support of leading Russian universities, project no. 5-100. The work by Gasnikov was supported by the Russian Foundation for Basic Research, project no. 18-31-20005 mol_a_ved (the main part of the paper) and by the Russian Science Foundation, project 17-11-01027 (the Appendix).
Received: 08.11.2017
Revised: 08.11.2017
Accepted: 11.03.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 7, Pages 1085–1097
DOI: https://doi.org/10.1134/S0965542519070078
Bibliographic databases:
Document Type: Article
UDC: 519.85
Language: Russian
Citation: A. V. Gasnikov, A. I. Turin, “Fast gradient descent for convex minimization problems with an oracle producing a (δ,L)-model of function at the requested point”, Zh. Vychisl. Mat. Mat. Fiz., 59:7 (2019), 1137–1150; Comput. Math. Math. Phys., 59:7 (2019), 1085–1097
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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