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Fundamentalnaya i Prikladnaya Matematika, 2014, Volume 19, Issue 5, Pages 49–73
(Mi fpm1605)
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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. 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.
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
Linking options:
https://www.mathnet.ru/eng/fpm1605 https://www.mathnet.ru/eng/fpm/v19/i5/p49
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