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On reduction of the two-stage problem of quantile optimization to the problem of convex programming

  • Stochastic Systems, Queueing Systems
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Abstract

Consideration was given to the two-stage problem of stochastic programming with a quantile criterion. The case of bilinear loss function which is linear separately in the normally distributed random factors and the strategies was studied. An algorithm was proposed based on solving the parametric problem of convex programming with the scalar parameter selected with the use of the dichotomy method. The solution proved to be guaranteeing for the original problem. An example was discussed.

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References

  1. Yudin, D.B., Zadachi i metody stokhasticheskogo programmirovaniya (Problems and Methods of Stochastic Programming), Moscow: Sovetskoe Radio, 1979.

    MATH  Google Scholar 

  2. Birge, J. and Louveaux, F., Introduction in Stochastic Programming, New York: Shpringer, 1997.

    Google Scholar 

  3. Malyshev, V.V. and Kibzun, A.I., Analiz i sintez vysokotochnogo upravleniya letatel’nymi apparatami (High-precision Control of Flight Vehicles: Analysis and Design), Moscow: Mashinostroenie, 1987.

    Google Scholar 

  4. Kibzun, A.I. and Kan, Yu.S., Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Problems of Stochastic Programming with Probabilistic Criteria), Moscow: Fizmatlit, 2009.

    MATH  Google Scholar 

  5. Kibzun, A.I. and Naumov, A.V., A Two-Stage Quantile Linear Programming Problem, Autom. Remote Control, 1995, vol. 56, no. 1, part 1, pp. 68–76.

    MATH  MathSciNet  Google Scholar 

  6. Naumov, A.V. and Bobylev, I.M., On the Two-Stage Problem of Linear Stochastic Programming with Quantile Criterion and Discrete Distribution of the Random Parameters, Autom. Remote Control, 2012, vol. 73, no. 2, pp. 265–275.

    Article  Google Scholar 

  7. Kibzun, A.I., Naumov, A.V., and Norkin, V.I., On Reducing a Quantile Optimization Problem with Discrete Distribution to a Mixed Integer Programming Problem, Autom. Remote Control, 2013, vol. 74, no. 6, pp. 951–967.

    Article  Google Scholar 

  8. Kibzun, A.I. and Khromova, O.M., On Reduction of the Multistage Problem of Stochastic Programming with Quantile Criterion to the Problem of Mixed Integer Linear Programming, Autom. Remote Control, 2014, vol. 75, no. 4, pp. 688–699.

    Article  Google Scholar 

  9. Kibzun, A.I. and Naumov, A.V., Guaranteeing Algorithm for Solution of the Quantile Optimization Problem, Kosm. Issled., 1995, vol. 33, no. 2, pp. 160–165.

    Google Scholar 

  10. Gol’shtein, E.G., Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya (Duality Theory in Mathematical Programming and Its Applications), Moscow: Nauka, 1971.

    Google Scholar 

  11. Dem’yanov, V.F. and Vasil’ev, L.V., Nedifferentsiruemaya optimizatsiya (Nondifferentiable Optimization), Moscow: Fizmatlit, 1981.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow State Aviation Institute, Moscow, Russia

    A. I. Kibzun & O. M. Khromova

Authors
  1. A. I. Kibzun
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  2. O. M. Khromova
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Correspondence to A. I. Kibzun.

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Original Russian Text © A.I. Kibzun, O.M. Khromova, 2014, published in Avtomatika i Telemekhanika, 2014, No. 5, pp. 67–82.

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Kibzun, A.I., Khromova, O.M. On reduction of the two-stage problem of quantile optimization to the problem of convex programming. Autom Remote Control 75, 859–871 (2014). https://doi.org/10.1134/S0005117914050051

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  • DOI: https://doi.org/10.1134/S0005117914050051

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