Email this article On the Proof of Pontryagin’s Maximum Principle by Means of Needle Variations
- Authors: Dmitruk A.V.1,2, Osmolovskii N.P.3,4,5
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Affiliations:
- Central Economics and Mathematics Institute, Russian Academy of Sciences
- Lomonosov Moscow State University
- University of Technology and Humanities in Radom
- Systems Research Institute, Polish Academy of Sciences
- Moscow State University of Civil Engineering
- Issue: Vol 218, No 5 (2016)
- Pages: 581-598
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/238263
- DOI: https://doi.org/10.1007/s10958-016-3044-2
- ID: 238263
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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.
About the authors
A. V. Dmitruk
Central Economics and Mathematics Institute, Russian Academy of Sciences; Lomonosov Moscow State University
Author for correspondence.
Email: dmitruk@member.ams.org
Russian Federation, Moscow; Moscow
N. P. Osmolovskii
University of Technology and Humanities in Radom; Systems Research Institute, Polish Academy of Sciences; Moscow State University of Civil Engineering
Email: dmitruk@member.ams.org
Poland, Radom; Warsaw; Moscow
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