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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 4, Pages 523–534
DOI: https://doi.org/10.7868/S0044466916040098 (Mi zvmmf10368) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Efficient numerical methods for entropy-linear programming problems

A. V. Gasnikovab, E. V. Gasnikovac, Yu. E. Nesterovd, A. V. Chernovc

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University "Higher School of Economics" (HSE), Moscow
c Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
d Center for Operat. Research and Econometrics Universite Catholigue de Louvain, Belgium
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DOI: https://doi.org/10.7868/S0044466916040098
Abstract: Entropy-linear programming (ELP) problems arise in various applications. They are usually written as the maximization of entropy (minimization of minus entropy) under affine constraints. In this work, new numerical methods for solving ELP problems are proposed. Sharp estimates for the convergence rates of the proposed methods are established. The approach described applies to a broader class of minimization problems for strongly convex functionals with affine constraints.
Key words: entropy-linear programming, fast gradient method, regularization, dual problem.
Funding agency Grant number
Russian Foundation for Basic Research 15-31-70001_мол_а_мос
14-01-00722_а
15-31-20571_мол_а_вед
Russian Science Foundation 14-50-00150
Gasnikova, Nesterov, and Chernov acknowledge the support of the Russian Foundation for Basic Research, project nos. 15-31-70001 mol_a_mos, 14-01-00722-a, and 15-31-20571-mol_a_ved. Theorem 2 was proved at the Institute for Information Transmission Problems of the Russian Academy of Sciences by Gasnikov, who acknowledges the support of the Russian Science Foundation, project no. 14-50-00150.
Received: 04.03.2015
Revised: 28.05.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 4, Pages 514–524
DOI: https://doi.org/10.1134/S0965542516040084
Bibliographic databases:
Document Type: Article
UDC: 519.658
Language: Russian
Citation: A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, A. V. Chernov, “Efficient numerical methods for entropy-linear programming problems”, Zh. Vychisl. Mat. Mat. Fiz., 56:4 (2016), 523–534; Comput. Math. Math. Phys., 56:4 (2016), 514–524
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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