Skip to main content
Log in

A theorem of convex polyhedra in connection with the problem of finding the set of solutions to a system of linear inequalities

  • Published:
Ukrainian Mathematical Journal Aims and scope

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.

Literature cited

  1. A. Charnes, Econometrica,20, No. 2, 160–170 (1952).

    Google Scholar 

  2. A. Charnes, W. S. Cooper, and A. Henderson, An Introduction to Linear Programming [Kussian translation], Moscow (1960); English edition: Wiley, New York (1953).

  3. A. W. Tucker, “Linear inequalities and convex polyhedral sets,” Proc. Second Symposium...., Washington, D. C. (1955), pp. 569–600.

  4. G. Sh. Rubinshtein, Uspekhi Matem. Nauk,9, No. 2, 171–178 (1954).

    Google Scholar 

  5. A. J. Goldman and A. W. Tucker, “Polyhedral convex cones,” Linear Inequalities and Related Systems (H. W. Kuhn and A. W. Tucker, editors), Princeton, U.P. (1956), pp. 19–40.

    Google Scholar 

  6. E. Ya. Remez, General Computational Methods of Chebyshev Approximation [in Russian], Izd. AN UkrSSR, Kiev (1957).

    Google Scholar 

  7. P. Alexandroff and J. Hopf, Topologie, Berlin (1935).

  8. S. N. Chernikov, Zh. Vyschisl. Matem. i Matem. Fiz.,5, No. 1, 3–20 (1965).

    Google Scholar 

  9. T. S. Motzkin, H. Raiffa, G. L. Thompson, and R. M. Thrall, “The double description method,” Contributions to the Theory of Games, Princeton, U. P. (1953), pp. 51–73.

    Google Scholar 

  10. E. Burger, Z. Angew. Math. Mech.,36, No.3/4, 135–139 (1956).

    Google Scholar 

  11. E. Ya. Remez, Dokl. Akad. Nauk SSSR,160, No.6, 1265–1268 (1965).

    Google Scholar 

  12. A. W. Tucker, Condensed Schemata for Dantzig's Simplex Method, Princeton, U. P. (1958).

    Google Scholar 

  13. E. L. Stiefel, Numer. Math.,2, 1–17 (1960).

    Google Scholar 

  14. S. Vajda, “The theory of games and linear programming,” Collection: Linear Inequalities and Related Systems [Russian translation], IL (1959), pp. 11–106; English edition: The Theory of Games and Linear Programming, Wiley, New York (1956).

    Google Scholar 

  15. D. B. Yudin and E. G. Gol'dshtein, Problems and Methods of Linear Programming [in Russian], Moscow (1961).

  16. C. Berge, Theory of Graphs and Its Applications [Russian translation], Moscow (1962); (Methuen) Barnes and Noble [English translation], New York (1962).

  17. D. König, Theorie der endlichen und unendlichen, Leipzig (1936); Theory of Finite and Infinite Graphs, New York (1950).

  18. G. Tarry, Nouv. Ann. Math.,14, 187–190 (1895).

    Google Scholar 

  19. M. Balinsky, J. Soc. Ind. Appl. Math.,9, No. 1, 72–88.

  20. G. Hadley, Linear Programming, Reading, Mass. (1962).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 19, No. 2, pp. 74–89, March–April, 1967.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Remez, E.Y., Shteinberg, A.S. A theorem of convex polyhedra in connection with the problem of finding the set of solutions to a system of linear inequalities. Ukr Math J 19, 191–202 (1967). https://doi.org/10.1007/BF01086830

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01086830

Keywords

Navigation