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Matematicheskie Zametki, 2017, Volume 102, Issue 4, Pages 565–578
DOI: https://doi.org/10.4213/mzm11310 (Mi mzm11310) 		 
This article is cited in 8 scientific papers (total in 8 papers)

On Optimal Harvesting of a Resource on a Circle

M. I. Zelikinab, L. V. Lokoutsievskiyab, S. V. Skopintcevc

a Lomonosov Moscow State University
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c State Budget Professional Educational Institution of Moscow "Vorobyovy Gory", Moscow
Full-text PDF (551 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm11310
Abstract: This paper studies the optimality in the problem of cyclic harvesting of a resource distributed on a circle with a certain prescribed density. The velocity of motion of the collecting device and the fraction of the resource harvested at a given time play the role of control. The problem is to choose a control maximizing a given quality functional. The paper presents the maximum principle for this (infinite-dimensional) problem. The maximum principle can be written as two inequalities which can be conveniently verified. The class of problems with a concave profit function is solved completely. At the end of the paper, several examples are considered to illustrate the developed technique.
Keywords: cyclic harvesting of a resource, maximum principle, spatially distributed resource, necessary conditions for optimality.
Received: 07.07.2016
Revised: 23.01.2017
English version:
Mathematical Notes, 2017, Volume 102, Issue 4, Pages 521–532
DOI: https://doi.org/10.1134/S0001434617090243
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: M. I. Zelikin, L. V. Lokoutsievskiy, S. V. Skopintcev, “On Optimal Harvesting of a Resource on a Circle”, Mat. Zametki, 102:4 (2017), 565–578; Math. Notes, 102:4 (2017), 521–532
Citation in format AMSBIB
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\vol 102
\issue 4
\pages 565--578
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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