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Convergence of Discrete Approximations of Stochastic Programming Problems with Probabilistic Criteria

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Discrete Optimization and Operations Research (DOOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

We consider stochastic programming problems with probabilistic and quantile objective functions. The original distribution of the random variable is replaced by a discrete one. We thus consider a sequence of problems with discrete distributions. We suggest conditions, which guarantee that the sequence of optimal strategies converges to an optimal strategy of the original problem. We consider the case of a symmetrical distribution, the case of the loss function increasing in the random variable, and the case of the loss function increasing in the optimization strategy.

S.V. Ivanov—Supported by Russian Science Foundation (project 15-11-10009).

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Author information

Authors and Affiliations

  1. Moscow Aviation Institute, Volokolamskoe Shosse 4, A-80, GSP-3, Moscow, Russia, 125993

    Andrey I. Kibzun & Sergey V. Ivanov

  2. Sobolev Institute of Mathematics, Acad. Koptyug Avenue, 4, Novosibirsk, Russia, 630090

    Sergey V. Ivanov

Authors
  1. Andrey I. Kibzun
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  2. Sergey V. Ivanov
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Corresponding author

Correspondence to Sergey V. Ivanov .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

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© 2016 Springer International Publishing Switzerland

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Kibzun, A.I., Ivanov, S.V. (2016). Convergence of Discrete Approximations of Stochastic Programming Problems with Probabilistic Criteria. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_41

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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