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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 10, Pages 1733–1749
DOI: https://doi.org/10.7868/S0044466916100057 (Mi zvmmf10471) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set

Yu. A. Chernyaev

Kazan National Research Technical University, Kazan, Tatarstan, Russia
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DOI: https://doi.org/10.7868/S0044466916100057
Abstract: The gradient projection method and Newton's method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary extremum conditions are examined, and the convergence of the methods is analyzed.
Key words: spherical surface, convex closed set, gradient projection method, Newton's method, necessary conditions for a local minimum, convergence of an algorithm.
Received: 21.10.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 10, Pages 1716–1731
DOI: https://doi.org/10.1134/S0965542516100055
Bibliographic databases:
Document Type: Article
UDC: 519.658
Language: Russian
Citation: Yu. A. Chernyaev, “Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016), 1733–1749; Comput. Math. Math. Phys., 56:10 (2016), 1716–1731
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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