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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 3, Pages 344–349 (Mi zvmmf9882)  

This article is cited in 7 scientific papers (total in 7 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

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.

DOI: https://doi.org/10.7868/S0044466913030162

Full text: PDF file (370 kB)
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Bibliographic databases:

UDC: 519.658
MSC: 65D15
Received: 14.12.2011
Revised: 06.09.2012

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{http://elibrary.ru/item.asp?id=18822252}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. K. Arutyunova, “Modifikatsiya metoda Evtushenko poiska globalnogo minimuma dlya sluchaya nepreryvnoi na otrezke funktsii”, Vestnik Kazanskogo gosudarstvennogo tekhnicheskogo universiteta im. A.N. Tupoleva, 69:2-2 (2013), 154–157  elib
    2. N. K. Arutyunova, A. M. Dulliev, V. I. Zabotin, “Algorithms for projecting a point onto a level surface of a continuous function on a compact set”, Comput. Math. Math. Phys., 54:9 (2014), 1395–1401  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Yu. A. Chernyaev, “An extension of the gradient projection method and Newton's method to extremum problems constrained by a smooth surface”, Comput. Math. Math. Phys., 55:9 (2015), 1451–1460  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Yu. A. Chernyaev, “Numerical algorithm for solving mathematical programming problems with a smooth surface as a constraint”, Comput. Math. Math. Phys., 56:3 (2016), 376–381  mathnet  crossref  crossref  isi  elib
    5. N. K. Arutyunova, A. M. Dulliev, V. I. Zabotin, “Models and methods for three external ballistics inverse problems”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:4 (2017), 78–91  mathnet  crossref  elib
    6. Yu. A. Chernyaev, “Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set”, Comput. Math. Math. Phys., 57:10 (2017), 1607–1615  mathnet  crossref  crossref  isi  elib  elib
    7. V. I. Zabotin, P. A. Chernyshevsky, “Extension of Strongin's global optimization algorithm to a function continuous on a compact interval”, Kompyuternye issledovaniya i modelirovanie, 11:6 (2019), 1111–1119  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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