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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2021, Volume 14, Issue 3, Pages 33–45
DOI: https://doi.org/~ 10.14529/mmp210303 https://doi.org/~ 10.14529/mmp210303
(Mi vyuru605)
 

Mathematical Modeling

Application of the smooth approximation of the probability function in some applied stochastic programming problems

V. R. Sobolab, R. O. Torishnyya, A. M. Pokhvalenskayaa

a JSC Expert RA, Moscow, Russian Federation
b Moscow Aviation Institute, Moscow, Russian Federation
References:
Abstract: This paper is devoted to the application of the smooth approximation of the probability function in the solution of three different stochastic optimization problems: minimization of an airstrip area under the constrained probability of successful landing, minimization of the cost of water supply system with random performance and with predefined water consumption, and determination of the set of wind speed vectors which guarantees the safe landing of an aircraft in future with the given probability. The first two problems are mathematical programming problems with probability constraint, and the third one is a problem of constructing the isoquant surface of the probability function. Smooth approximation of the probability function allows to use the gradient projection method in the constrained optimization problem and to define the isoquant surface as the solution to a partial differential equation. We provide an example for each of the considered problems and compare the results with known results previously obtained using the confidence method.
Keywords: stochastic programming, probability function, sigmoid function, gradient projection method.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-90035
The reported research was funded by RFBR, project number 20-31-90035.
Received: 27.04.2021
Document Type: Article
UDC: 519.856
MSC: 90C15
Language: English
Citation: V. R. Sobol, R. O. Torishnyy, A. M. Pokhvalenskaya, “Application of the smooth approximation of the probability function in some applied stochastic programming problems”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:3 (2021), 33–45
Citation in format AMSBIB
\Bibitem{SobTorPok21}
\by V.~R.~Sobol, R.~O.~Torishnyy, A.~M.~Pokhvalenskaya
\paper Application of the smooth approximation of the probability function in some applied stochastic programming problems
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2021
\vol 14
\issue 3
\pages 33--45
\mathnet{http://mi.mathnet.ru/vyuru605}
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