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

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Fundamentalnaya i Prikladnaya Matematika, 2014, Volume 19, Issue 5, Pages 49–73 (Mi fpm1605)

This article is cited in 8 scientific papers (total in 8 papers)

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

A. V. Dmitruk^ab, N. P. Osmolovskii^cd

^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

Full-text PDF (241 kB) Citations (8)

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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.

English version:
Journal of Mathematical Sciences (New York), 2016, Volume 218, Issue 5, Pages 581–598
DOI: https://doi.org/10.1007/s10958-016-3044-2

Bibliographic databases:

Document Type: Article

UDC: 517.977.52

Language: Russian

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

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\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://mathscinet.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}

Linking options:

https://www.mathnet.ru/eng/fpm1605

https://www.mathnet.ru/eng/fpm/v19/i5/p49

This publication is cited in the following 8 articles:

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
Francesca Calà Campana, Alfio Borzì, “On the SQH Method for Solving Differential Nash Games”, J Dyn Control Syst, 28:4 (2022), 739
S. Hofmann, A. Borzì, “A sequential quadratic hamiltonian algorithm for training explicit RK neural networks”, Journal of Computational and Applied Mathematics, 405 (2022), 113943
Tim Breitenbach, Alfio Borzì, “A Sequential Quadratic Hamiltonian Method for Solving Parabolic Optimal Control Problems with Discontinuous Cost Functionals”, J Dyn Control Syst, 25:3 (2019), 403
Tim Breitenbach, Alfio Borzì, “On the SQH Scheme to Solve Nonsmooth PDE Optimal Control Problems”, Numerical Functional Analysis and Optimization, 40:13 (2019), 1489
A. V. Dmitruk, N. P. Osmolovskii, “Variations of the $v$-change of time in problems with state constraints”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S49–S64
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
S. Roy, A. Borzi, “Numerical investigation of a class of Liouville control problems”, J. Sci. Comput., 73:1 (2017), 178–202

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	79

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