Skip to main content
SpringerLink
Log in

High-order necessary optimality conditions in a linear maxmin problem with coupled variables

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

For a linear maxmin problem with equality constraints, a theorem is proved that provides a basis for constructing an efficient algorithm for its solution.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. G. Gol’shtein, Duality Theory in Mathematical Programming and Its Aplications (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  2. R. Gabasov, F. M. Kirillova, and A. I. Tyatyushkin, Constructive Optimization Methods, Part 1: Linear Problems (Universitetskoe, Minsk, 1984) [in Russian].

    Google Scholar 

  3. Yu. P. Ivanilov, “Dual Semigames,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 4, 3–9 (1972).

    Google Scholar 

  4. J. E. Falk, “Linear Maxmin Problem,” Math. Program. 5(2), 169–188 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. R. Mamatov, “A Dual Algorithm for Finding a Local Optimum in a Linear Maxmin Problem with Coupled Variables,” Uzbekskii Zh. Probl. Informatiki Energ., No. 1 (2001).

  6. A. R. Mamatov, “On Duality Theory for Linear Maxmin Problem with Coupled Variables,” Sib. Zh. Vychisl. Mat. 10 (2), 181–187 (2007).

    Google Scholar 

  7. A. R. Mamatov, “On a Game Problem with Coupled Variables,” Dokl. Uzb. Akad. Nauk, No. 7, 7–13 (1993).

    Google Scholar 

  8. V. V. Fedorov, Numerical Maxmin Methods (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  9. I. Azizov, A Finite Algorithm for Linear Maxmin Problem with Coupled Variables and Numerical Results, Preprint No. 18(203) (Institute of Mathematics, Belarussian Academy of Sciences, Minsk, 1984).

    Google Scholar 

  10. D. D. Lozovanu, “Maxmin Problems with Coupled Variables and Their Application For the Investigation and Solution of Cyclic Games,” Izv. Akad. Nauk Moldavskoi SSR. Mat., No. 2, 22–29 (1990).

    MathSciNet  Google Scholar 

  11. A. R. Mamatov, “A n Algorithm for Solving a Linear Maxmin Problem with Coupled Variables,” Zh. Vychisl. Mat. Mat. Fiz. 45, 1044–1047 (2005) [Comput. Math. Math. Phys. 45, 1006-1010 (2005)].

    MATH  MathSciNet  Google Scholar 

  12. A. R. Mamatov, “A n Algorithm for Solving a Two-Person Game with Information Transfer,” Zh. Vychisl. Mat. Mat. Fiz. 46, 1784–1789 (2006) [Comput. Math. Math. Phys. 46, 1699-1704 (2006)].

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Higher Military Automotive Command Engineering School, Samarkand, 703056, Uzbekistan

    A. R. Mamatov

Authors
  1. A. R. Mamatov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. R. Mamatov.

Additional information

Original Russian Text © A.R. Mamatov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 6, pp. 1017–1022.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mamatov, A.R. High-order necessary optimality conditions in a linear maxmin problem with coupled variables. Comput. Math. and Math. Phys. 50, 963–968 (2010). https://doi.org/10.1134/S0965542510060047

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542510060047

Search

Navigation