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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, Volume 26, Number 3, Pages 101–117
DOI: https://doi.org/10.21538/0134-4889-2020-26-3-101-117 (Mi timm1749) 		 
This article is cited in 3 scientific papers (total in 3 papers)

A Criterion for the Existence of Nondestructive Controls in the Problem of Optimal Exploitation of a Binary-Structured System

V. D. Mazurov, A. I. Smirnov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (284 kB) Citations (3)
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DOI: https://doi.org/10.21538/0134-4889-2020-26-3-101-117
Abstract: Earlier the authors proved the equivalence of a sustainable exploitation problem for a system of renewable resources and a certain mathematical program. In this paper we study the properties of a map describing the dependence of the state vector of the system on the control. In the particular case of a structured population described by the binary Leslie model, conditions for the objective function are characterized under which there are optimal controls preserving all structural divisions of the system. In this case, we use the notion of local irreducibility, which generalizes the classical notion of map irreducibility.
Keywords: optimal exploitation of ecosystems, nondestructive controls, irreducible map, concave programming.
Funding agency Grant number
Russian Foundation for Basic Research 19-07-01243
This work was supported by the Russian Foundation for Basic Research (project no. 19-07-01243).
Received: 11.06.2020
Revised: 20.07.2020
Accepted: 24.07.2020
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2021, Volume 315, Issue 1, Pages S203–S218
DOI: https://doi.org/10.1134/S008154382106016X
Bibliographic databases:
Document Type: Article
UDC: 519.853+517.988.523
MSC: 47N05, 37N25, 37N40
Language: Russian
Citation: V. D. Mazurov, A. I. Smirnov, “A Criterion for the Existence of Nondestructive Controls in the Problem of Optimal Exploitation of a Binary-Structured System”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 3, 2020, 101–117; Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S203–S218
Citation in format AMSBIB
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\vol 26
\issue 3
\pages 101--117
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