Skip to main content
Log in

Optimization and Identification of Stochastic Systems*

  • SYSTEMS ANALYSIS
  • Published:
Cybernetics and Systems Analysis Aims and scope

The author overviews some well-known scientific results from the theory of stochastic optimization and theory of risk, obtained by the Academician of the National Academy of Sciences of Ukraine Y. M. Ermoliev and his colleagues and students. Examples from the theory of parametric and non-parametric estimation are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Yu. M. Ermoliev, Stochastic Programming Methods [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  2. Yu. M. Ermoliev and R. Wets (eds.), Techniques for Stochastic Optimization, Springer, Berlin (1988).

    MATH  Google Scholar 

  3. Yu. M. Kaniovskii, P. S. Knopov, and Z. V. Nekrylova, Limiting Theorems for Stochastic Programming Processes [in Russian], Naukova Dumka, Kyiv (1980).

    Google Scholar 

  4. Y. M. Ermoliev and V. I. Norkin, “On nonsmooth and discontinuous problems of stochastic systems optimization,” Europ. J. Oper. Res., No. 2, 230–243 (1997).

  5. Y. Ermoliev and G. Leonardi, “Some proposals for stochastic facility locations models,” Mathem. Model., Vol. 5, No. 5, 407–420 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Keyzer and Y. Ermoliev, “Modeling producer decisions in a spatial continuum,” in: P. Herings, G. Van der Laan, and A. Talman (eds.), The Theory of Markets, North-Holland, Amsterdam–Oxford–New York (1999), pp. 281–305.

  7. Y. Ermoliev and C. Nedeva, “Stochastic optimization problem with partially known distribution functions,” Intern. In-t for App. Systems Analysis, CP-82-060, Laxenburg (1982).

  8. Yu. Ermoliev, A. Gaivoronski, and S. Nedeva, “Stochastic optimization problems with incomplete information on distribution functions,” SIAM J. Control Optim., Vol. 23, No. 56, 697–716 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  9. V. I. Norkin, G. Ch. Pflug, and A. Ruszczynski, “A branch and bound method for stochastic global optimization,” Math. Program., Vol. 83, 425–450 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  10. Y. M. Ermoliev and V. I. Norkin, “Stochastic optimization of risk functions,” in: K. Marti, Y. Ermoliev, and G. Pflug (eds.), Dynamic Stochastic Optimization, Berlin–Heidelberg–Springer, (2004), pp. 225–247.

  11. P. S. Knopov and I. V. Sergienko, “Some scientific results of Yu. M. Ermoliev and his school in modern stochastic optimization theory,” Cybern. Syst. Analysis, Vol. 47, No. 6, 835–853 (2011). https://doi.org/10.1007/s10559-011-9363-x.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. S. Knopov and E. I. Kasitskaya, “Large deviations of empirical estimates in stochastic programming problems,” Cybern. Syst. Analysis, Vol. 40, No. 4, 510–516 (2004). https://doi.org/10.1023/B:CASA.0000047872.23833.35.

    Article  MathSciNet  MATH  Google Scholar 

  13. P. S. Knopov and E. J. Kasitskaya, “Properties of empirical estimates in stochastic optimization and identification problems,” Annals of Operations Research, Vol. 56, No. 1, 225–239 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  14. P. S. Knopov, “Asymptotic properties of some classes of M-estimates,” Cybern. Syst. Analysis, Vol. 33, No. 4, 468–481 (1997). https://doi.org/10.1007/BF02733103.

    Article  MathSciNet  MATH  Google Scholar 

  15. P. S. Knopov and E. J. Kasitskaya, “On large deviations of empirical estimates in a stochastic programming problem with time-dependent observations,” Cybern. Syst. Analysis, Vol. 46, No. 5, 724–728 (2010). https://doi.org/10.1007/s10559-010-9253-7.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. N. Golodnikov, Yu. M. Ermoliev, and P. S. Knopov, “Estimating reliability parameters under insufficient information,” Cybern. Syst. Analysis, Vol. 46, No. 3, 443–459 (2010). https://doi.org/10.1007/s10559-010-9219-9.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. N. Golodnikov, P. S. Knopov, and V. A. Pepelyaev, “Estimation of reliability parameters under incomplete primary information,” Theory and Decision, Vol. 57, No. 4, 331–344 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  18. P. S. Knopov and V. A. Pepelyaev, “Nonparametric estimate of almost periodic signals,” Cybern. Syst. Analysis, Vol. 43, No. 3, 362–367 (2007). https://doi.org/10.1007/s10559-007-0057-3.

    Article  MathSciNet  MATH  Google Scholar 

  19. Yu. M. Ermoliev, T. Y. Ermolieva, G. J. MacDonald, and V. I. Norkin, “Insurability of catastrophic risks: The stochastic optimization model,” Optimization, Vol. 47, 251–265 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  20. Y. M. Ermoliev, T. Y. Ermolieva, G. MacDonald, and V. I. Norkin, “Stochastic optimization of insurance portfolios for managing exposure to catastrophic risks,” Annals Oper. Res., Vol. 99, 207–225 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  21. V. S. Mikhalevich, P. S. Knopov, and A. N. Golodnikov, “Mathematical models and methods of riks assessment in ecologically hazardous industries,” Cybern. Syst. Analysis, Vol. 30, No. 2, 259–273 (1994). https://doi.org/10.1007/BF02366429.

    Article  MATH  Google Scholar 

  22. A. N. Golodnikov, Yu. M. Ermol’ev, T. Yu. Ermol’eva, P. S. Knopov, and V. A. Pepelyaev, “Integrated modeling of food security management in Ukraine. I. Models for management of the economic availability of food,” Cybern. Syst. Analysis, Vol. 49, No. 1, 26–35 (2013). https://doi.org/10.1007/s10559-013-9481-8.

  23. A. N. Golodnikov, Yu. M. Ermol’ev, T. Yu. Ermol’eva, P. S. Knopov, and V. A. Pepelyaev, “Integrated modeling of food security management in Ukraine. II. Models for structural optimization of agricultural production under risk,” Cybern. Syst. Analysis, Vol. 49, No. 2, 217–228 (2013). https://doi.org/10.1007/s10559-013-9503-6.

  24. K. Marti, Yu. Ermoliev, and M. Makowski, “Coping with uncertainty. Robust solutions,” in: Lecture Notes in Economics and Mathematical Systems, Springer, Berlin–Heidelberg (2010).

  25. V. A. Pepelyaev and N. A. Golodnikova, “Mathematical methods for crop losses risk evaluation and account for sown areas planning,” Cybern. Syst. Analysis, Vol. 50, No. 1, 60–67 (2014). https://doi.org/10.1007/s10559-014-9592-x.

    Article  Google Scholar 

  26. V. I. Norkin, A. A. Gaivoronski, V. A. Zaslavsky, and P. S. Knopov, “Models of the optimal resource allocation for the critical infrastructure protection,” Cybern. Syst. Analysis, Vol. 54, No. 5, 696–706 (2018). https://doi.org/10.1007/s10559-018-0071-7.

    Article  MATH  Google Scholar 

  27. A. A. Gaivoronski, Y. M. Ermoliev, P. S. Knopov, and V. I. Norkin, “Mathematical modeling of distributed catastrophic and terrorist,” Cybern. Syst. Analysis, Vol. 51, No. 1, 85–95 (2015). https://doi.org/10.1007/s10559-015-9700-6.

    Article  MATH  Google Scholar 

  28. Yu. Ermoliev, T. Ermolieva, T. Kahil, M. Obersteiner, V. Gorbachuk, and P. Knopov, “Stochastic optimization models for risk-based reservoir management,” Cybern. Syst. Analysis, Vol. 55, No. 1, 55–64 (2019). https://doi.org/10.1007/s10559-019-00112-z.

    Article  MathSciNet  MATH  Google Scholar 

  29. V. A. Pepelyaev, A. N. Golodnikov, and N. A. Golodnikova, “Reliability optimization in plant production,” Cybern. Syst. Analysis, Vol. 58, No. 2, 191–196 (2022). https://doi.org/10.1007/s10559-022-00450-5.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. S. Knopov.

Additional information

*The study was partially supported by the National Research Foundation of Ukraine, Grant No. 2020.02/0121.

Translated from Kibernetyka ta Systemnyi Analiz, No. 3, May–June, 2023, pp. 21–32.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Knopov, P.S. Optimization and Identification of Stochastic Systems*. Cybern Syst Anal 59, 375–384 (2023). https://doi.org/10.1007/s10559-023-00572-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-023-00572-4

Keywords

Navigation