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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 3, Pages 344–349
DOI: https://doi.org/10.7868/S0044466913030162 (Mi zvmmf9882) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Two algorithms for finding the projection of a point onto a nonconvex set in a normed space

V. I. Zabotin, N. K. Arutyunova

Kazan State Technical University
Full-text PDF (370 kB) Citations (8)
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DOI: https://doi.org/10.7868/S0044466913030162
Abstract: Two iteration algorithms are proposed for finding the projection of a point onto a nonconvex set in a normed space, which is given by $f(x) = 0$ equation. For the first case the left hand side of this equation is supposed to satisfy the subordination condition, which generalizes the Lipshitz condition. For the second casethe continuity of $f$ function is supposed and an approximate algorithm of projection is constructed.
Key words: projection algorithm; algorithm convergence; Lipshitz condition; nonconvex surface.
Received: 14.12.2011
Revised: 06.09.2012
Bibliographic databases:
Document Type: Article
UDC: 519.658
MSC: 65D15
Language: Russian
Citation: V. I. Zabotin, N. K. Arutyunova, “Two algorithms for finding the projection of a point onto a nonconvex set in a normed space”, Zh. Vychisl. Mat. Mat. Fiz., 53:3 (2013), 344–349
Citation in format AMSBIB
\Bibitem{ZabAru13}
\by V.~I.~Zabotin, N.~K.~Arutyunova
\paper Two algorithms for finding the projection of a point onto a nonconvex set in a normed space
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
\issue 3
\pages 344--349
\mathnet{http://mi.mathnet.ru/zvmmf9882}
\crossref{https://doi.org/10.7868/S0044466913030162}
\zmath{https://zbmath.org/?q=an:06188982}
\elib{https://elibrary.ru/item.asp?id=18822252}
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  • https://www.mathnet.ru/eng/zvmmf/v53/i3/p344
    • This publication is cited in the following 8 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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    Full-text PDF :82
    References:58
    First page:21
     
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