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On necessary conditions for an extremum for nondifferentiable functions

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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).

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Additional information

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

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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

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