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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Volume 291, Pages 215–230
DOI: https://doi.org/10.1134/S0371968515040160 (Mi tm3676) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Pontryagin maximum principle. Ab ovo usque ad mala

G. G. Magaril-Il'yaevab

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (263 kB) Citations (2)
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DOI: https://doi.org/10.1134/S0371968515040160
Abstract: A proof of the Pontryagin maximum principle for a sufficiently general optimal control problem is presented; the proof is based on the implicit function theorem and the theorem on the solvability of a finite-dimensional system of nonlinear equations. The exposition is self-contained: all necessary preliminary facts are proved. These facts are mainly related to the properties of solutions to differential equations with discontinuous right-hand side and are derived as corollaries to the implicit function theorem, which, in turn, is a direct consequence of Newton's method for solving nonlinear equations.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12447
14-01-00456
14-01-00744
This work was supported by the Russian Foundation for Basic Research, project nos. 13-01-12447, 14-01-00456, and 14-01-00744.
Received: December 15, 2014
English version:
Proceedings of the Steklov Institute of Mathematics, 2015, Volume 291, Pages 203–218
DOI: https://doi.org/10.1134/S0081543815080167
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
Language: Russian
Citation: G. G. Magaril-Il'yaev, “The Pontryagin maximum principle. Ab ovo usque ad mala”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 215–230; Proc. Steklov Inst. Math., 291 (2015), 203–218
Citation in format AMSBIB
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\paper The Pontryagin maximum principle. Ab ovo usque ad mala
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 215--230
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968515040160}
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\pages 203--218
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    • This publication is cited in the following 2 articles:
    1. A. V. Dmitruk, “Variations of v-change of time in an optimal control problem with state and mixed constraints”, Izv. Math., 87:4 (2023), 726–767  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. E. R. Avakov, G. G. Magaril-Il'yaev, “Generalized Needles and Second-Order Conditions in Optimal Control”, Proc. Steklov Inst. Math., 304 (2019), 8–25  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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