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Deterministic equivalents for the problems of stochastic programming with probabilistic criteria

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Abstract

Consideration was given to the problems of stochastic programming with probabilistic and quantile criteria. For some special cases, deterministic equivalents of the original stochastic problems were constructed. The convex properties of the probabilistic and quantile criteria were established for the problems under study.

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References

  1. Yudin, D.B., Matematicheskie metody upravleniya v usloviyakh nepolnoi informatsii (Mathematical Methods of Control under Incomplete Information), Moscow: Sovetskoe Radio, 1974.

    Google Scholar 

  2. Kibzun, A.I. and Kan, Yu.S., Stochastic Programming Problems with Probability and Quantile Functions, Chichester: Wiley, 1996.

    MATH  Google Scholar 

  3. Kan, Yu.S. and Kibzun, A.I., Properties of Convexity of the Probability and Quantile Functions in the Optimization Problems, Avtom. Telemekh., 1996, no. 3, pp. 82–102.

  4. Polyak, B.T., Vvedenie v optimizatsiyu (Introduction to Optimization), Moscow: Nauka, 1980.

    Google Scholar 

  5. Symonds, G.H., Deterministic Solution for a Class of Chance-constrained Programming Problems, Oper. Res., 1967, vol. 15, no. 3, pp. 495–512.

    Article  MATH  MathSciNet  Google Scholar 

  6. Rajk, E., On the Quantile Function in the Stochastic Nonlinear Programming, Izv. AN ESSR, Fiz.-mat., 1971, vol. 20, no. 1, pp. 229–231.

    MATH  Google Scholar 

  7. Lepp, R., Deterministic Equivalents of the Problem of Stochastic Programming with Elliptically Symmetrical Distributions, Izv. AN ESSR, Fiz.-mat., 1979, vol. 28, no. 2, pp. 158–160.

    MATH  MathSciNet  Google Scholar 

  8. Tamm, E., On Quasiconcavity of the Probability and Quantile Functions, Izv. AN ESSR, Fiz.-mat., 1976, vol. 25, no. 2, pp. 141–143.

    MATH  MathSciNet  Google Scholar 

  9. Kan, Yu.S. and Tuzov, N.V., Minimization of the Quantile of the Normal Distribution of the Bilinear Loss Function, Avtom. Telemekh., 1998, no. 11, pp. 82–92.

  10. Prékopa, A., Contributions to the Theory of Stochastic Programming, Math. Program., 1973, no. 64, pp. 202–221.

  11. Prékopa, A., Logarithmic Concave Measures and Related Topics, in Stochastic Programming, Dempster, M.A.H., Ed., New York: Academic, 1980, pp. 63–82.

    Google Scholar 

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Original Russian Text © V.B. Vishnaykov, A.I. Kibzun, 2006, published in Avtomatika i Telemekhanika, 2006, No. 6, pp. 126–143.

This paper was recommended for publication by A.V. Nazin, a member of the Editorial Board

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Vishnaykov, V.B., Kibzun, A.I. Deterministic equivalents for the problems of stochastic programming with probabilistic criteria. Autom Remote Control 67, 945–961 (2006). https://doi.org/10.1134/S0005117906060099

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  • DOI: https://doi.org/10.1134/S0005117906060099

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