Geodesic
Programmed iteration method and operator convexity in an abstract retention problem
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 3, pp. 348-366

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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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     author = {D. A. Serkov and A. G. Chentsov},
     title = {Programmed iteration method and operator convexity in an abstract retention problem},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {348--366},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2015_25_3_a4/}
}
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D. A. Serkov; A. G. Chentsov. Programmed iteration method and operator convexity in an abstract retention problem. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 3, pp. 348-366. http://geodesic.mathdoc.fr/item/VUU_2015_25_3_a4/