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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2017, Volume 23, Number 3, Pages 134–143
DOI: https://doi.org/10.21538/0134-4889-2017-23-3-134-143
(Mi timm1444)
 

This article is cited in 8 scientific papers (total in 8 papers)

Sample average approximation in the two-stage stochastic linear programming problem with quantile criterion

S. V. Ivanov, A. I. Kibzun

Moscow Aviation Institute (National Research University)
Full-text PDF (207 kB) Citations (8)
References:
Abstract: The two-stage problem of stochastic linear programming with quantile criterion is considered. In this problem, the first stage strategy is deterministic and the second stage strategy is chosen when a realization of the random parameters is known. The properties of the problem are studied, a theorem on the existence of its solution is proved, and a sample average approximation of the problem is constructed. The sample average approximation is reduced to a mixed integer linear programming problem, and a theorem on their equivalence is proved. A procedure for finding an optimal solution of the approximation problem is suggested. A theorem on the convergence of discrete approximations with respect to the value of the objective function and to the optimization strategy is given. We also consider some cases not covered in the theorem.
Keywords: stochastic programming, quantile criterion, sample average approximation, mixed integer linear programming.
Funding agency Grant number
Russian Foundation for Basic Research 17-07-00203А
Received: 19.05.2017
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2018, Volume 303, Issue 1, Pages 115–123
DOI: https://doi.org/10.1134/S0081543818090122
Bibliographic databases:
Document Type: Article
UDC: 519.856
MSC: 90C15
Language: Russian
Citation: S. V. Ivanov, A. I. Kibzun, “Sample average approximation in the two-stage stochastic linear programming problem with quantile criterion”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 3, 2017, 134–143; Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 115–123
Citation in format AMSBIB
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\by S.~V.~Ivanov, A.~I.~Kibzun
\paper Sample average approximation in the two-stage stochastic linear programming problem with quantile criterion
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 3
\pages 134--143
\mathnet{http://mi.mathnet.ru/timm1444}
\crossref{https://doi.org/10.21538/0134-4889-2017-23-3-134-143}
\elib{https://elibrary.ru/item.asp?id=29938006}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2018
\vol 303
\issue , suppl. 1
\pages 115--123
\crossref{https://doi.org/10.1134/S0081543818090122}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000453521100012}
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  • https://www.mathnet.ru/eng/timm/v23/i3/p134
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    Full-text PDF :78
    References:35
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