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Avtomat. i Telemekh., 2019, Issue 6, Pages 70–90 (Mi at15118)  

Stochastic Systems

General properties of two-stage stochastic programming problems with probabilistic criteria

S. V. Ivanov, A. I. Kibzun

Moscow Aviation Institute (National Research University), Moscow, Russia

Abstract: Two-stage stochastic programming problems with the probabilistic and quantile criteria in the general statement are considered. Sufficient conditions for the measurability of the loss function and also for the semicontinuity of the criterion functions are given. Sufficient conditions for the existence of optimal strategies are established. The equivalence of the a priori and a posteriori statements of the problems under study is proved. The application of the confidence method, which consists in the transition to a deterministic minimax problem, is described and justified. Sample approximations of the problems are constructed and also conditions under which the optimal strategies in the approximating problems converge to the optimal strategy in the original problem are presented. The results are illustrated by an example of the linear two-step problem. The two-stage problem with the probabilistic criterion is reduced to a mixed-integer problem.

Keywords: stochastic programming, two-stage problem, probabilistic criterion, quantile criterion.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-07-00203_
This work was supported by the Russian Foundation for Basic Research, project no. 17-07-00203A.


DOI: https://doi.org/10.1134/S0005231019060047

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English version:
Automation and Remote Control, 2019, 80:6, 1041–1057

Bibliographic databases:

Document Type: Article

Received: 27.08.2018
Revised: 21.01.2019
Accepted: 07.02.2019

Citation: S. V. Ivanov, A. I. Kibzun, “General properties of two-stage stochastic programming problems with probabilistic criteria”, Avtomat. i Telemekh., 2019, no. 6, 70–90; Autom. Remote Control, 80:6 (2019), 1041–1057

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