Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On necessary conditions for an extremum for nondifferentiable functions

  • 21 Accesses

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

Literature Cited

  1. 1.

    A. Ya. Dubovitskii and A. A. Milyutin, “Constrained extremum problems,” Zh. Vychisl. Mat. Mat. Fiz.,5, No. 3 (dy1965).

  2. 2.

    H. Halkin and L. W. Neustadt, “General necessary conditions for optimization problems,” Proc. Nat. Acad. Sci.,56 (1966).

  3. 3.

    B. N. Pshenichnyi, Necessary Conditions for an Extremum [in Russian], Nauka, Moscow (1969).

  4. 4.

    A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).

  5. 5.

    E. A. Nurminskii, “Quasigradient method for solving linear programming problems,” Kibernetika, No. 1 (1973).

  6. 6.

    N. Z. Shor, “On a class of almost differentiable functions and a method of minimizing functions of this class,” Kibernetika, No. 4 (1972).

  7. 7.

    F. H. Clarke, “Generalized gradients and applications,” Trans. Am. Math. Soc.,205 (1975).

  8. 8.

    R. Mifflin, “Semismooth and semiconvex functions in constrained optimization,” RR-76-21, J. JASA (1976).

  9. 9.

    A. D. Ioffe and V. M. Tikhomirov, “Duality of convex functions and extremal problems,” Usp. Mat. Nauk,23, No. 6, 51–116 (1968).

  10. 10.

    R. T. Rockafellar, Convex Analysis, Princeton University Press (1970).

  11. 11.

    A. A. Milyutin, “Theory of conditions for higher order extrema for constrained extrenum problems,” in: Proceedings of All-Union Symposium on Optimal Control and Differential Games, Tbilisi (1977).

  12. 12.

    B. N. Pshenichnyi, “Necessary conditions for an extremum for differential inclusions,” Kibernetika, No. 6 (1976).

Download references

Additional information

Translated from Kibernetika, No. 6, pp. 92–96, November–December, 1977.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pshenichnyi, B.N. On necessary conditions for an extremum for nondifferentiable functions. Cybern Syst Anal 13, 886–891 (1977). https://doi.org/10.1007/BF01068855

Download citation

Keywords

  • Operating System
  • Artificial Intelligence
  • System Theory
  • Nondifferentiable Function