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Stochastic quasigradient algorithm to minimize the quantile function

  • Stochastic Systems
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Abstract

A stochastic quasigradient algorithm to minimize the quantile function on the basis of order statistic was proposed, and its convergence with the probability one was proved. An example was considered.

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References

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

    Google Scholar 

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

    Google Scholar 

  3. Kibzun, A.I. and Kurbakovkiy, V.Yu., Guaranteeing Approach to Solving Quantile Optimization Problems, Ann. Oper. Res., 1991, vol. 30, pp. 81–93.

    Article  MATH  MathSciNet  Google Scholar 

  4. Kan, Yu.S., Quasigradient Algorithm to Minimize the Quantile function, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1996, no. 2, pp. 81–86.

    Google Scholar 

  5. Kan, Yu.S., On Convergence of a Stochastic Quasigradient Algorithm of Quantile Optimization, Autom. Remote Control, 2003, no. 2, pp. 263–278.

    Article  MathSciNet  Google Scholar 

  6. Lepp, R., Stochastic Approximation Type Algorithm for the Maximization of the Probability function, Eesti NSV Teaduste Akademia Toimetised, Füüsika, Matem., 1983, vol. 32, no. 2, pp. 150–156.

    MATH  MathSciNet  Google Scholar 

  7. David, H.A. and Nagaraja, H.N., Order Statistics, New Jersey: Wiley, 2003.

    Book  MATH  Google Scholar 

  8. Reiss, R.D., Approximate Distributions of Order Statistics, New York: Springer, 1989, pp. 207–212.

    MATH  Google Scholar 

  9. Mikhalevich, V.S., Gupal, A.M., and Norkin, V.I., Metody nevypukloi optimizatsii (Methods of Noncon-vex Optimization), Moscow: Nauka, 1987.

    Google Scholar 

  10. Ermol’ev, Yu.M., Metody stokhasticheskogo programmirovaniya (Methods of Stochastic Programming), Moscow: Nauka, 1976.

    MATH  Google Scholar 

  11. Kan, Yu.S. and Kibzun, A.I., Convexity Properties of Probability and Quantile Functions in Optimization Problems, Autom. Remote Control, 1996, no. 3, part 1, pp. 368–383.

    MathSciNet  Google Scholar 

  12. Prekopa, A., On Logarithmic Concave Measures and Functions, Acta Scientiarum Math., 1973, vol. 34, pp. 335–343.

    MATH  MathSciNet  Google Scholar 

  13. Shiryaev, A.N., Veroyatnost’—1 (Probability—1), Moscow: MTSNMO, 2004.

    Google Scholar 

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Authors and Affiliations

  1. Moscow State Aviation Institute, Moscow, Russia

    A. I. Kibzun & E. L. Matveev

Authors
  1. A. I. Kibzun
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  2. E. L. Matveev
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Additional information

Original Russian Text © A.I. Kibzun, E.L. Matveev, 2010, published in Avtomatika i Telemekhanika, 2010, No. 6, pp. 64–78.

This work was supported by the Russian Foundation for Basic Research, project no. 09-08-00369.

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Kibzun, A.I., Matveev, E.L. Stochastic quasigradient algorithm to minimize the quantile function. Autom Remote Control 71, 1034–1047 (2010). https://doi.org/10.1134/S0005117910060056

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  • DOI: https://doi.org/10.1134/S0005117910060056

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