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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 1979, Volume 19, Number 1, Pages 70–78 (Mi zvmmf5442)  
Methods for solving constrained extremum problems in the presence of random noise

B. T. Polyak

Moskva
Full-text PDF (1008 kB)
Abstract: 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.
Received: 19.12.1975
English version:
USSR Computational Mathematics and Mathematical Physics, 1979, Volume 19, Issue 1, Pages 72–81
DOI: https://doi.org/10.1016/0041-5553(79)90067-3
Bibliographic databases:
Document Type: Article
UDC: 519, 517.977
MSC: Primary 90C31; Secondary 90C30
Language: Russian
Citation: B. T. Polyak, “Methods for solving constrained extremum problems in the presence of random noise”, Zh. Vychisl. Mat. Mat. Fiz., 19:1 (1979), 70–78; U.S.S.R. Comput. Math. Math. Phys., 19:1 (1979), 72–81
Citation in format AMSBIB
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\by B.~T.~Polyak
\paper Methods for solving constrained extremum problems in the presence of random noise
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1979
\vol 19
\issue 1
\pages 70--78
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=525467}
\zmath{https://zbmath.org/?q=an:0406.90067}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1979
\vol 19
\issue 1
\pages 72--81
\crossref{https://doi.org/10.1016/0041-5553(79)90067-3}
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