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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 3, Pages 74–79 (Mi ivm8786)  

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

Brief communications

One approach to constructing cutting algorithms with dropping of cutting planes

I. Ya. Zabotina, R. S. Yarullinb

a Chair of Data Analysis and Operation Research, Kazan (Volga Region) Federal University, Kazan, Russia
b Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: We propose a general cutting method for conditional minimization of continuous functions. We calculate iteration points by partially immersing the admissible set in approximating polyhedral sets. We describe the features of the proposed method and prove its convergence. The constructed general method does not imply the inclusion of each of approximating sets in the previous one. This feature allows us to construct cutting algorithms which periodically drop any additional restrictions which occur in the solution process.

Keywords: conditional minimization, approximating set, cutting plane, algorithm, sequence of approximations, convergence.

Full text: PDF file (159 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:3, 60–64

UDC: 519.853
Presented by the member of Editorial Board: Я. И. Заботин
Received: 19.07.2012

Citation: I. Ya. Zabotin, R. S. Yarullin, “One approach to constructing cutting algorithms with dropping of cutting planes”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 3, 74–79; Russian Math. (Iz. VUZ), 57:3 (2013), 60–64

Citation in format AMSBIB
\Bibitem{ZabYar13}
\by I.~Ya.~Zabotin, R.~S.~Yarullin
\paper One approach to constructing cutting algorithms with dropping of cutting planes
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 3
\pages 74--79
\mathnet{http://mi.mathnet.ru/ivm8786}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 3
\pages 60--64
\crossref{https://doi.org/10.3103/S1066369X13030092}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84876239464}


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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, R. S. Yarullin, “Metod otsechenii s obnovleniem pogruzhayuschikh mnozhestv i otsenki tochnosti resheniya”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2013, 54–64  mathnet
    2. I. Ya. Zabotin, R. S. Yarullin, “Algoritm otsechenii s approksimatsiei nadgrafika”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2013, 48–54  mathnet
    3. I. Ya. Zabotin, R. S. Yarullin, “Metod otsechenii s obnovleniem approksimiruyuschikh mnozhestv i ego kombinirovanie s drugimi algoritmami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 10 (2014), 13–26  mathnet
    4. 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
    5. I. Ya. Zabotin, R. S. Yarullin, “Cutting-plane method based on epigraph approximation with discarding the cutting planes”, Autom. Remote Control, 76:11 (2015), 1966–1975  mathnet  crossref  isi  elib  elib
    6. 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
    7. 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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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