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Derivation of the necessary conditions for an extremum in the optimal control problem

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Literature Cited

  1. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York (1962).

    Google Scholar 

  2. L. W. Neustadt, “An abstract variational theory with applications to a broad class of optimization problems. 1: General theory,” SIAM J. Control, 4, No. 3 (1966).

    Google Scholar 

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

  4. B. N. Pshenichnyi, Necessary Conditions for an Extremum, Marcel Dekker Inc., New York (1971).

    Google Scholar 

  5. A. D. Dubovitskii and A. A. Milyutin, “Translation of Euler's equation,” Zh. Vychisl. Matem. i Matem. Fiz.,9, No. 6 (1969).

  6. V. I. Arkin and V. A. Levin, “The convexity of the values of vector integrals,” Usp. Matem. Nauk,27, No. 3(165) (1972).

  7. A. A. Lyapunov, “On completely additive vector functions,” Izv. Akad. Nauk SSSR, Matematika,4, No. 6 (1940).

  8. N. Dunford and J. T. Schwartz, Linear Operators, Wiley-Interscience, New York (1957).

    Google Scholar 

  9. R. V. Gamkrelidze, “On sliding optimal states,” Dokl. Akad. Nauk SSSR,143, No. 6, (1962).

  10. L. A. Lyusternik (Liusternik) and V. I. Sobolev, Elements of Functional Analysis. F. Ungar, New York (1961).

    Google Scholar 

  11. V. I. Arkin, “On the infinite analog of the nonconvex programming problem,” Kibernetika, No. 2, (1967).

  12. A. Ya. Dubovitskii and A. A. Milyutin, “Extremum problems in the presence of restrictions,” Zh. Vychisl. Matem. i Matem. Fiz.,5, No. 3 (1965).

  13. V. G. Boltyanskii, Mathematical Methods of Optimal Control, Holt, Rinehart, and Winston, New York (1971).

    Google Scholar 

  14. P. I. Mysovskikh, “Necessary conditions for the extremum of set functions under constraints,” Latviisk. Mat. Ezhegod., No. 14 (1974).

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Authors
  1. P. I. Mysovskikh
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Translated from Kibernetika, No. 1, pp. 116–123, January–February, 1975.

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Mysovskikh, P.I. Derivation of the necessary conditions for an extremum in the optimal control problem. Cybern Syst Anal 11, 132–142 (1975). https://doi.org/10.1007/BF01069958

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  • DOI: https://doi.org/10.1007/BF01069958

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