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Home » Issues » Archive of Issues » 2015 - 3 issue » pp. 348-366

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Russia Yekaterinburg
Year
2015
Volume
25
Issue
3
Pages
348-366
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Section Mathematics
Title Programmed iteration method and operator convexity in an abstract retention problem
Author(-s) Serkov D.A.ab, Chentsov A.G.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
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
UDC 517.977
MSC 37N35, 65J15, 47J25, 52A01, 91A25
DOI 10.20537/vm150305
Received 30 June 2015
Language Russian
Citation Serkov D.A., Chentsov A.G. Programmed iteration method and operator convexity in an abstract retention problem, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 3, pp. 348-366.
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