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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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\issue 4
\pages 565--578
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  • https://doi.org/10.4213/mzm11310
  • https://www.mathnet.ru/eng/mzm/v102/i4/p565
    • This publication is cited in the following 8 articles:
    1. L. I. Rodina, A. V. Chernikova, “Ob optimalnoi dobyche vozobnovlyaemogo resursa na beskonechnom promezhutke vremeni”, Tr. IMM UrO RAN, 29, no. 1, 2023, 167–179  mathnet  crossref  mathscinet  elib
    2. Dmitry Gromov, Tadashi Shigoka, Anton Bondarev, “Optimality and sustainability of hybrid limit cycles in the pollution control problem with regime shifts”, Environ Dev Sustain, 26:4 (2023), 10701  crossref
    3. Yilun Wu, Anna Tur, Hongbo Wang, “Sustainable Optimal Control for Switched Pollution-Control Problem with Random Duration”, Entropy, 25:10 (2023), 1426  crossref
    4. A. Davydov, E. Vinnikov, “Optimal cyclic dynamic of distributed population under permanent and impulse harvesting”, Dynamic Control and Optimization, Springer Proceedings in Mathematics & Statistics, 407, 2022, 101  crossref
    5. A. V. Egorova, “Optimizatsiya diskontirovannogo dokhoda dlya strukturirovannoi populyatsii, podverzhennoi promyslu”, Vestnik rossiiskikh universitetov. Matematika, 26:133 (2021), 15–25  mathnet
    6. Upmann T., Behringer S., “Harvesting a Remote Renewable Resource”, Theor. Ecol., 13:4 (2020), 459–480  crossref  isi
    7. S. Anita, S. Behringer, A.-M. Mosneagu, T. Upmann, “Optimal harvesting of a spatially distributed renewable resource with endogenous pricing”, Math. Model. Nat. Phenom., 14:1 (2019), UNSP 101  crossref  mathscinet  isi  scopus
    8. A. V. Egorova, L. I. Rodina, “Ob optimalnoi dobyche vozobnovlyaemogo resursa iz strukturirovannoi populyatsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 501–517  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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