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Avtomatika i Telemekhanika, 2018, Issue 2, Pages 19–35
(Mi at15014)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/at15014 https://www.mathnet.ru/eng/at/y2018/i2/p19
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Statistics & downloads: |
Abstract page: | 297 | Full-text PDF : | 33 | References: | 27 | First page: | 17 |
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