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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 9, Pages 1448–1454 (Mi zvmmf10086)  

This article is cited in 6 scientific papers (total in 6 papers)

Algorithms for projecting a point onto a level surface of a continuous function on a compact set

N. K. Arutyunova, A. M. Dulliev, V. I. Zabotin

Kazan National Research Technological University, ul. Karla Marksa 10, Kazan, 420111, Tatarstan, Russia

Abstract: Given an equation $f(x)=0$, the problem of finding its solution nearest to a given point is considered. In contrast to the authors’ previous works dealing with this problem, exact algorithms are proposed assuming that the function $f$ is continuous on a compact set. The convergence of the algorithms is proved, and their performance is illustrated with test examples.

Key words: $\varepsilon$-Lipschitz continuity, projection of a point onto a level surface, nonconvex set, solution of a nonlinear equation.

DOI: https://doi.org/10.7868/S0044466914090038

Full text: PDF file (299 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2014, 54:9, 1395–1401

Bibliographic databases:

UDC: 519.658
Received: 10.11.2013

Citation: 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”, Zh. Vychisl. Mat. Mat. Fiz., 54:9 (2014), 1448–1454; Comput. Math. Math. Phys., 54:9 (2014), 1395–1401

Citation in format AMSBIB
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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. 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
    2. 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
    3. 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
    4. 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
    5. 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
    6. V. I. Zabotin, P. A. Chernyshevskii, “Dve modifikatsii obobschennogo metoda Piyavskogo poiska globalnogo minimuma nepreryvnoi na otrezke funktsii i ikh skhodimost”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2021, no. 3, 70–85  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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