Skip to main content
SpringerLink
Log in

The Pontryagin Maximum Principle and Sufficient Optimality Conditions for Nonlinear Problems

  • Published:
Differential Equations Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  1. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal'nykh protsessov (Mathematical Theory of Optimal Processes), Moscow, 1969.

  2. Ekeland, I., Math.Anal.Appl., 1974, vol. 47, no. 2, pp. 324–353.

    Google Scholar 

  3. Danzer, L., Grünbaum, B., and Klee, V., Helly's Theorem and Its Relatives, Proc. Sympos. Pure Math., Vol. VII, pp. 101–180, Providence: AMS, 1963. Translated under the title Teorema Khelli i ee primeneniya, Moscow: Mir, 1968.

    Google Scholar 

  4. Halmos, P., Lectures on Ergodic Theory, Chicago, 1956. Translated under the title Lektsii po ergodicheskoi teorii, Moscow: Inostrannaya Literatura, 1959.

    Google Scholar 

  5. Peetre, J. and Spaar, G., Ann.Mat.Pura Appl., 1972, vol. 92, pp. 217–262.

    Google Scholar 

  6. Levitin, E.S., Milyutin, A.A., and Osmolovskii, N.P., Uspekhi Mat.Nauk, 1978, vol. 33, no. 6, pp. 85–148.

    Google Scholar 

  7. Arutyunov, A.V. and Vinter, R.B., Differents.Uravn., 2003, vol. 39, no. 11, pp. 1443–1451.

    Google Scholar 

  8. Arutyunov, A.V., Usloviya ekstremuma.Anormal'nye i vyrozhdennye zadachi (Extremum Conditions. Abnormal and Degenerate Problems), Moscow, 1997.

  9. Arutyunov, A.V., Itogi Nauki i Tekhniki.Mat.Analiz, 1989, vol. 27, pp. 147–235.

    Google Scholar 

  10. Alekseev, V.M., Tikhomirov, V.M., and Fomin, S.V., Optmal'noe upravlenie (Optimal Control), Moscow, 1979.

  11. Arutyunov, A.V., Dokl.RAN, 2000, vol. 371, no. 1, pp. 10–13.

    Google Scholar 

  12. Gamkrelidze, R.V., Osnovy optimal'nogo upravleniya (Foundations of Optimal Control Theory), Tbilisi, 1977.

Download references

Author information

Authors and Affiliations

  1. Friendship of Nations University, Moscow, Russia

    A. V. Arutyunov

Authors
  1. A. V. Arutyunov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arutyunov, A.V. The Pontryagin Maximum Principle and Sufficient Optimality Conditions for Nonlinear Problems. Differential Equations 39, 1671–1679 (2003). https://doi.org/10.1023/B:DIEQ.0000023546.85791.0c

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:DIEQ.0000023546.85791.0c

Keywords

Search

Navigation