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Avtomat. i Telemekh., 2018, Issue 2, Pages 19–35 (Mi at15014)  

This article is cited in 6 scientific papers (total in 6 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

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.


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English version:
Automation and Remote Control, 2018, 79:2, 216–228

Bibliographic databases:

Presented by the member of Editorial Board: Б. М. Миллер

Received: 20.03.2017

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
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\issue 2
\pages 19--35
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\transl
\jour Autom. Remote Control
\yr 2018
\vol 79
\issue 2
\pages 216--228
\crossref{https://doi.org/10.1134/S0005117918020029}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ivanov V S., Kibzun I A., Stepanova A.S., “An Algorithm to Solve a Quantile Optimization Problem With Loss Function Having a Separable Structure, and Its Application to An Aerospace Problem”, Appl. Stoch. Models. Bus. Ind.  crossref  isi
    2. S. V. Ivanov, “A bilevel stochastic programming problem with random parameters in the Follower's objective function”, J. Appl. Industr. Math., 12:4 (2018), 658–667  mathnet  crossref  crossref  elib
    3. S. V. Ivanov, A. I. Kibzun, N. Mladenović, “Variable neighborhood search for a two-stage stochastic programming problem with a quantile criterion”, Autom. Remote Control, 80:1 (2019), 43–52  mathnet  crossref  crossref  isi  elib
    4. Ivanov S.V., Kibzun A.I., Mladenovic N., Urosevic D., “Variable Neighborhood Search For Stochastic Linear Programming Problem With Quantile Criterion”, J. Glob. Optim., 74:3 (2019), 549–564  crossref  isi
    5. S. N. Vasil'eva, Yu. S. Kan, “Approximation of probabilistic constraints in stochastic programming problems with a probability measure kernel”, Autom. Remote Control, 80:11 (2019), 2005–2016  mathnet  crossref  crossref  isi  elib
    6. S. V. Ivanov, A. I. Kibzun, “General properties of two-stage stochastic programming problems with probabilistic criteria”, Autom. Remote Control, 80:6 (2019), 1041–1057  mathnet  crossref  crossref  isi  elib
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