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Avtomatika i Telemekhanika, 2018, Issue 2, Pages 19–35 (Mi at15014)  

This article is cited in 13 scientific papers (total in 13 papers)

On the convergence of sample approximations for stochastic programming problems with probabilistic criteria

S. V. Ivanov, A. I. Kibzun

Moscow Aviation Institute (National State University), Moscow, Russia
References:
Abstract: We consider stochastic programming problems with probabilistic and quantile criteria. We describe a method for approximating these problems with a sample of realizations for random parameters. When we use this method, criterial functions of the problems are replaced with their sample estimates. We show the hypoconvergence of sample probability functions to its exact value that guarantees the convergence of approximations for the probability function maximization problem on a compact set with respect to both the value of the criterial function and the optimization strategy. We prove a theorem on the convergence of approximation for the quantile function minimization problem with respect to the value of the criterial function and the optimization strategy.
Keywords: quantile criterion, probabilistic criterion, sample approximation, hypoconvergence.
Funding agency Grant number
Russian Foundation for Basic Research 17-07-00203A
Ministry of Education and Science of the Russian Federation 2.2461.2017/4.6
The work of S. V. Ivanov has been supported by the Russian Foundation for Basic Research, project no. 17-07-00203A. The work of A. I. Kibzun was done as part of the state assignment of the Russian Ministry of Science and Education, project no. 2.2461.2017/4.6.
Presented by the member of Editorial Board: B. M. Miller

Received: 20.03.2017
English version:
Automation and Remote Control, 2018, Volume 79, Issue 2, Pages 216–228
DOI: https://doi.org/10.1134/S0005117918020029
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. V. Ivanov, A. I. Kibzun, “On the convergence of sample approximations for stochastic programming problems with probabilistic criteria”, Avtomat. i Telemekh., 2018, no. 2, 19–35; Autom. Remote Control, 79:2 (2018), 216–228
Citation in format AMSBIB
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\by S.~V.~Ivanov, A.~I.~Kibzun
\paper On the convergence of sample approximations for stochastic programming problems with probabilistic criteria
\jour Avtomat. i Telemekh.
\yr 2018
\issue 2
\pages 19--35
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\jour Autom. Remote Control
\yr 2018
\vol 79
\issue 2
\pages 216--228
\crossref{https://doi.org/10.1134/S0005117918020029}
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  • https://www.mathnet.ru/eng/at15014
  • https://www.mathnet.ru/eng/at/y2018/i2/p19
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Avtomatika i Telemekhanika
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