FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 3, PAGES 921-942

A. G. Chentsov

Abstract

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```
Two abstract versions of the programmed iterations method are
considered. This method was used in the theory of differential
games for constructing the value function and the stable bridges
in the sense of N. N. Krasovskii. The connection of the direct
version of the programmed iterations method and the known iterated
procedure operating in the space of sets is investigated. The
direct iterated procedure is realized in the space of set-valued
mappings. For the indirect iterated procedure the natural process
of the compression of phase constraints is realized; the corresponding
goal set is fixed. The duality of two above-mentioned versions
of the programmed iterations method is established.
```

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Last modified: February 17, 2003