Geodesic
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

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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. 
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     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},
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     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_1_a6/}
}
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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/