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Tr. Mat. Inst. Steklova, 2001, Volume 233, Pages 71–88 (Mi tm225)  

This article is cited in 11 scientific papers (total in 11 papers)

The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval

S. M. Aseevab, A. V. Kryazhimskiiba, A. M. Tarasyevcb

a Steklov Mathematical Institute, Russian Academy of Sciences
b International Institute for Applied Systems Analysis
c Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A class of nonlinear optimal control problems with infinite time interval is investigated that arise in mathematical economics. Necessary conditions of optimality in the form of the Pontryagin maximum principle are obtained that contain additional conditions on the adjoint function and on the behavior of the Hamiltonian at infinity. In some cases, these additional conditions guarantee the validity of the usual transversality conditions at infinity.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 233, 64–80

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received in December 2000

Citation: S. M. Aseev, A. V. Kryazhimskii, A. M. Tarasyev, “The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval”, Differential equations. Certain mathematical problems of optimal control, Collected papers, Tr. Mat. Inst. Steklova, 233, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 71–88; Proc. Steklov Inst. Math., 233 (2001), 64–80

Citation in format AMSBIB
\Bibitem{AseKryTar01}
\by S.~M.~Aseev, A.~V.~Kryazhimskii, A.~M.~Tarasyev
\paper The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval
\inbook Differential equations. Certain mathematical problems of optimal control
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2001
\vol 233
\pages 71--88
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm225}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1866978}
\zmath{https://zbmath.org/?q=an:1021.49016}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 233
\pages 64--80


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    This publication is cited in the following articles:
    1. Nikol'skii M.S., “Investigation of the continuity and Lipschitz properties for the Bellman function in some optimization problems on the semi-infinite interval $[0,+\infty)$”, Differ. Equ., 38:11 (2002), 1599–1604  mathnet  crossref  mathscinet  isi  scopus  scopus
    2. Nikol'skii M.S., “On a nonlinear optimal investment problem”, Differ. Equ., 39:11 (2003), 1603–1608  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Weber T.A., “Infinite-horizon optimal advertising in a market for durable goods”, Optimal Control Appl. Methods, 26:6 (2005), 307–336  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Weber T.A., “An infinite-horizon maximum principle with bounds on the adjoint variable”, Journal of Economic Dynamics & Control, 30:2 (2006), 229–241  crossref  mathscinet  zmath  isi  scopus  scopus
    5. S. M. Aseev, A. V. Kryazhimskii, “The Pontryagin Maximum Principle and Optimal Economic Growth Problems”, Proc. Steklov Inst. Math., 257 (2007), 1–255  mathnet  crossref  mathscinet  zmath  elib
    6. A. I. Smirnov, “Necessary Optimality Conditions for a Class of Optimal Control Problems with Discontinuous Integrand”, Proc. Steklov Inst. Math., 262 (2008), 213–230  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. Seierstad A., Sydaeter K., “Conditions implying the vanishing of the Hamiltonian at infinity in optimal control problems”, Optim. Lett., 3:4 (2009), 507–512  crossref  mathscinet  zmath  isi  scopus  scopus
    8. S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, “Infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 67:2 (2012), 195–253  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    10. D. V. Khlopin, “O neobkhodimykh kraevykh usloviyakh dlya silno optimalnogo upravleniya v zadachakh na beskonechnom promezhutke”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 1, 49–58  mathnet
    11. Khlopin D., “Necessity of Vanishing Shadow Price in Infinite Horizon Control Problems”, J. Dyn. Control Syst., 19:4 (2013), 519–552  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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