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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 3, Pages 348–366 (Mi vuu489)  

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Programmed iteration method and operator convexity in an abstract retention problem

D. A. Serkovab, A. G. Chentsovba

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Institute of Radioelectronics and Information Technologies, Ural Federal University named after the first President of Russia B. N. Yeltsin, ul. Mira, 32, Yekaterinburg, 620002, Russia

Abstract: For an abstract dynamic system the game problem of trajectories retention in a given set is considered. The relations of the method of programmed iterations and the constructions associated with the generation of the operator convex hull with the help of prehull are investigated. Within these relations the procedure of constructing the hull is realized in the form dual to the procedure based on the method of programmed iterations. The retention problem solution is determined in the class of multi-valued quasistrategies (nonanticipating responses to the realization of uncertain factors of the process). It is shown that the set of successful solvability of the retention problem is defined as the limit of the iterative procedure in the space of sets, elements of which are positions of the game; the structure of resolving quasistrategies is also provided.

Keywords: programmed iterations, operator convexity, quasistrategies.

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Document Type: Article
UDC: 517.977
MSC: 37N35, 65J15, 47J25, 52A01, 91A25
Received: 30.06.2015

Citation: D. A. Serkov, A. G. Chentsov, “Programmed iteration method and operator convexity in an abstract retention problem”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:3 (2015), 348–366

Citation in format AMSBIB
\Bibitem{SerChe15}
\by D.~A.~Serkov, A.~G.~Chentsov
\paper Programmed iteration method and operator convexity in an abstract retention problem
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 3
\pages 348--366
\mathnet{http://mi.mathnet.ru/vuu489}
\elib{http://elibrary.ru/item.asp?id=24237241}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Serkov, A. G. Chentsov, “The elements of the operator convexity in the construction of the programmed iteration method”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:3 (2016), 82–93  mathnet  crossref  elib
    2. D. A. Serkov, A. G. Chentsov, “Realizatsiya metoda programmnykh iteratsii v paketakh prostranstv”, Izv. IMI UdGU, 2016, no. 2(48), 42–67  mathnet  elib
    3. D. A. Serkov, “Transfinite sequences in the method of programmed iterations”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 153–164  mathnet  crossref  crossref  isi  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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