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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 9, Pages 1493–1502
DOI: https://doi.org/10.7868/S0044466915090082 (Mi zvmmf10262) 		 
This article is cited in 10 scientific papers (total in 10 papers)

An extension of the gradient projection method and Newton's method to extremum problems constrained by a smooth surface

Yu. A. Chernyaev

Kazan Typolev National Research Technical University, ul. Karla Marksa 10, Kazan, 420111, Tatarstan, Russia
Full-text PDF (543 kB) Citations (10)
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DOI: https://doi.org/10.7868/S0044466915090082
Abstract: The gradient projection method and Newton’s method are extended to the case where the constraints are nonconvex and are represented by a smooth surface. Necessary extremum conditions and the convergence of the methods are examined.
Key words: smooth surface, gradient projection method, Newton's method, projection on a nonconvex set, necessary condition for a local minimum, convergence of an algorithm.
Received: 22.04.2014
Revised: 17.12.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 9, Pages 1451–1460
DOI: https://doi.org/10.1134/S0965542515090079
Bibliographic databases:
Document Type: Article
UDC: 519.658
Language: Russian
Citation: Yu. A. Chernyaev, “An extension of the gradient projection method and Newton's method to extremum problems constrained by a smooth surface”, Zh. Vychisl. Mat. Mat. Fiz., 55:9 (2015), 1493–1502; Comput. Math. Math. Phys., 55:9 (2015), 1451–1460
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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