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

Dynamic programming and conditions of optimality of control of stochastic convex mappings

  • 17 Accesses

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

Literature Cited

  1. 1.

    V. I. Arkin and I. V. Evstingneev, Probabilistic Models of Control and Economic Dynamics [in Russian], Nauka, Moscow (1979).

  2. 2.

    V. L. Makarov and A. M. Rubinov, Mathematical Theory of Economic Dynamics and Equilibrium [in Russian], Nauka, Moscow (1973).

  3. 3.

    B. N. Pshenichnyi, Convex Analysis and Extremal Problems [in Russian], Nauka, Moscow (1980).

  4. 4.

    N. N. Bordunov, “Optimality conditions for multistep control of stochastic convex mappings,” Kibernetika, No. 1, 40–45 (1983).

  5. 5.

    B. N. Pshenichnyi, “Convex multivalued mappings and their conjugates,” Kibernetika, No. 3, 94–102 (1972).

  6. 6.

    R. Rockafellar and R. Wets, “Stochastic convex programming: relatively complete resource and induced feasibility,” SIAM, J. Control. Optim.,14, No. 3, 574–589 (1976).

  7. 7.

    V. V. Beresnev, “On optimal programs of systems of discrete inclusions with infinite operating time,” Kibernetika, No. 3, 93–99 (1978).

  8. 8.

    I. V. Evstigneev, “Measurable selection and dynamic programming,” Math. Oper. Res.,1, No. 3, 267–272 (1976).

  9. 9.

    R. Rockafellar and R. Wets, “Non-anticipativity and L1-martingales in stochastic optimization problems,” Math. Program. Study,6, 170–187 (1976).

  10. 10.

    E. B. Dynkin and A. A. Yushkevich, Controlled Markov Processes and Their Applications [in Russian], Nauka, Moscow (1975).

  11. 11.

    E. B. Dynkin and I. V. Evstigneev, “Regular conditional means of correspondences,” Teor. Veroyatn. Ee Primen.,21, No. 2, 334–347 (1976).

  12. 12.

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

  13. 13.

    L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

  14. 14.

    R. Rockafellar, “Integrals that are convex functionals, 2,” in: Mathematical Economics, Equilibrium Models, Optimum Planning and Control [Russian translation], Mir, Moscow (1974), pp. 170–204.

Download references

Additional information

Translated from Kibernetika, No. 2, pp. 51–55, March–April, 1984.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bordunov, N.N. Dynamic programming and conditions of optimality of control of stochastic convex mappings. Cybern Syst Anal 20, 233–239 (1984). https://doi.org/10.1007/BF01069178

Download citation


  • Operating System
  • Artificial Intelligence
  • System Theory
  • Dynamic Programming
  • Convex Mapping