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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2013, Volume 155, Book 4, Pages 48–54 (Mi uzku1240)  

This article is cited in 3 scientific papers (total in 3 papers)

A cutting plane algorithm with an approximation of an epigraph

I. Ya. Zabotin, R. S. Yarullin

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: For the conditional minimization problem, we propose a cutting plane algorithm with an approximation of the epigraph of the objective function. The algorithm makes it possible to update approximating sets by dropping the cutting planes which accumulate during the solution process. We prove the convergence of the algorithm and describe its properties.

Keywords: approximating set, cutting hyperplane, sequence of approximations, convergence, conditional minimization, epigraph.

Full text: PDF file (425 kB)
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UDC: 519.853
Received: 02.10.2013

Citation: I. Ya. Zabotin, R. S. Yarullin, “A cutting plane algorithm with an approximation of an epigraph”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 155, no. 4, Kazan University, Kazan, 2013, 48–54

Citation in format AMSBIB
\Bibitem{ZabYar13}
\by I.~Ya.~Zabotin, R.~S.~Yarullin
\paper A cutting plane algorithm with an approximation of an epigraph
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2013
\vol 155
\issue 4
\pages 48--54
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1240}


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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. I. Ya. Zabotin, O. N. Shulgina, R. S. Yarullin, “Metod otsechenii i postroenie na ego osnove smeshannykh algoritmov minimizatsii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 156, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2014, 14–24  mathnet
    2. I. Ya. Zabotin, O. N. Shul'gina, R. S. Yarullin, “Minimization method with approximation of constraint zone and epigraph of objective function”, Russian Math. (Iz. VUZ), 60:11 (2016), 78–81  mathnet  crossref  isi
    3. O. N. Shulgina, R. S. Yarullin, I. Ya. Zabotin, “A cutting method with approximation of a constraint region and an epigraph for solving conditional minimization problems”, Lobachevskii J. Math., 39:6 (2018), 847–854  crossref  mathscinet  zmath  isi  scopus
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