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Fundam. Prikl. Mat., 2014, Volume 19, Issue 5, Pages 49–73 (Mi fpm1605)  

This article is cited in 3 scientific papers (total in 3 papers)

On the proof of Pontryagin's maximum principle by means of needle variations

A. V. Dmitrukab, N. P. Osmolovskiicd

a Central Economics and Mathematics Institute RAS
b Lomonosov Moscow State University
c University of Technology and Humanities in Radom, Poland
d Moscow State University of Civil Engineering

Abstract: We propose a proof of the maximum principle for the general Pontryagin type optimal control problem, based on packets of needle variations. The optimal control problem is first reduced to a family of smooth finite-dimensional problems, the arguments of which are the widths of the needles in each packet, then, for each of these problems, the standard Lagrange multipliers rule is applied, and finally, the obtained family of necessary conditions is “compressed” in one universal optimality condition by using the concept of centered family of compacta.

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English version:
Journal of Mathematical Sciences (New York), 2016, 218:5, 581–598

Bibliographic databases:

Document Type: Article
UDC: 517.977.52

Citation: A. V. Dmitruk, N. P. Osmolovskii, “On the proof of Pontryagin's maximum principle by means of needle variations”, Fundam. Prikl. Mat., 19:5 (2014), 49–73; J. Math. Sci., 218:5 (2016), 581–598

Citation in format AMSBIB
\Bibitem{DmiOsm14}
\by A.~V.~Dmitruk, N.~P.~Osmolovskii
\paper On the proof of Pontryagin's maximum principle by means of needle variations
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 5
\pages 49--73
\mathnet{http://mi.mathnet.ru/fpm1605}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431892}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 218
\issue 5
\pages 581--598
\crossref{https://doi.org/10.1007/s10958-016-3044-2}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Dykhta, “Pozitsionnyi printsip minimuma dlya kvazioptimalnykh protsessov v zadachakh upravleniya s terminalnymi ogranicheniyami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 113–128  mathnet  crossref
    2. S. Roy, A. Borzi, “Numerical investigation of a class of Liouville control problems”, J. Sci. Comput., 73:1 (2017), 178–202  crossref  mathscinet  zmath  isi  scopus
    3. A. V. Dmitruk, N. P. Osmolovskii, “Variatsii tipa $v$-zameny vremeni v zadachakh s fazovymi ogranicheniyami”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 76–92  mathnet  crossref  elib
  • Фундаментальная и прикладная математика
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