Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 1, pp. 70-78
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B. T. Polyak. Methods for solving constrained extremum problems in the presence of random noise. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 1, pp. 70-78. http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_1_a6/
@article{ZVMMF_1979_19_1_a6,
author = {B. T. Polyak},
title = {Methods for solving constrained extremum problems in the presence of random noise},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {70--78},
year = {1979},
volume = {19},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_1_a6/}
}
TY - JOUR
AU - B. T. Polyak
TI - Methods for solving constrained extremum problems in the presence of random noise
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 1979
SP - 70
EP - 78
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_1_a6/
LA - ru
ID - ZVMMF_1979_19_1_a6
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%0 Journal Article
%A B. T. Polyak
%T Methods for solving constrained extremum problems in the presence of random noise
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1979
%P 70-78
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_1_a6/
%G ru
%F ZVMMF_1979_19_1_a6
The extemum problem with equation-type constraints is considered, when the measurements of all functions and their gradients are subject to noise. Three methods of solution are described: they are modifications of the method of Lagrange multipliers, the method of penalty functions, and the method of penalty estimates respectively. The methods are shown to be convergent in a specific probability sense.
