Skip to main content
Log in

Refined theorems on the relaxation of equality constraints in an optimal control problem, linear with respect to the control

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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. A. Milyutin, “On quadratic conditions for an extremum in smooth problems with a finite-dimensional image,” in: Methods of the Theory of Extremal Problems in Economics [in Russian], Nauka, Moscow (1981), pp. 138–177.

    Google Scholar 

  2. A. V. Dmitruk, “Quadratic conditions for the Pontryagin minimum in an optimal control problem, linear with respect to control. II. Theorems on the relaxation of equality constraints,” Izv. Akad. Nauk SSSR, Ser. Mat.,51, No. 4, 812–832 (1987).

    Google Scholar 

  3. A. V. Dmitruk, “Quadratic conditions for the Pontryagin minimum in an optimal control problem, linear with respect to control. I. A decoding theorem,” Izv. Akad. Nauk SSSR, Ser. Mat.,50, No. 2, 284–312 (1986).

    Google Scholar 

  4. E. S. Levitin, A. A. Milyutin and N. P. Osmolovskii, “Higher order conditions for a local minimum in problems with constraints,” Usp. Mat. Nauk,33, No. 6, 85–148 (1978).

    Google Scholar 

  5. E. S. Levitin, A. A. Milyutin, and N. P. Osmolovskii, “Theory of higher-order conditions in smooth problems on extremum with constraints,” in: Theoretical and Applied Problems in Optimal Control [in Russian], Nauka, Sib. Otd., Novosibirsk (1985), pp. 4–40.

    Google Scholar 

  6. L. A. Lyusternik, “On conditional extrema of functionals,” Mat. Sb.,41, No. 3, 390–401 (1934).

    Google Scholar 

  7. A. V. Dmitruk, A. A. Milyutin, and N. P. Osmolovskii, “Lyusternik's theorem and the theory of the extremum,” Usp. Mat. Nauk,35, No. 6, 11–46 (1980).

    Google Scholar 

  8. A. V. Dmitruk, “Quadratic conditions for the Pontryagin minimum in an optimal control problem that is linear with respect to control, with a constraint on the control,” Dokl. Akad. Nauk SSSR,272, No. 2, 285–289 (1983).

    Google Scholar 

Download references

Authors

Additional information

Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 2, pp. 37–51, March–April, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dmitruk, A.V. Refined theorems on the relaxation of equality constraints in an optimal control problem, linear with respect to the control. Sib Math J 31, 215–229 (1990). https://doi.org/10.1007/BF00970651

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970651

Keywords

Navigation