FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

**Some questions of the structure of the programmed iterations method**

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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published in Russian.

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Last modified: February 17, 2003