Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 3, Pages 74–79 (Mi ivm8786)  
This article is cited in 15 scientific papers (total in 15 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
Full-text PDF (159 kB) Citations (15)
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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.
Presented by the member of Editorial Board: Ya. I. Zabotin
Received: 19.07.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 3, Pages 60–64
DOI: https://doi.org/10.3103/S1066369X13030092
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
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
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\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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  • https://www.mathnet.ru/eng/ivm8786
  • https://www.mathnet.ru/eng/ivm/y2013/i3/p74
    • This publication is cited in the following 15 articles:
    1. I. Ya. Zabotin, O. N. Shulgina, R. S. Yarullin, “Relaksatsionnyi variant metoda otsechenii s approksimatsiei oblasti ogranichenii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 165, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2023, 143–152  mathnet  crossref
    2. Igor Zabotin, Oksana Shulgina, Rashid Yarullin, Communications in Computer and Information Science, 1881, Mathematical Optimization Theory and Operations Research: Recent Trends, 2023, 54  crossref
    3. I. Ya. Zabotin, K. E. Kazaeva, O. N. Shul'gina, “A cutting-plane method with internal iteration points for the general convex programming problem”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 165:3 (2023), 208–218  mathnet  mathnet  crossref
    4. Igor Zabotin, Oksana Shulgina, Rashid Yarullin, Communications in Computer and Information Science, 1661, Mathematical Optimization Theory and Operations Research: Recent Trends, 2022, 218  crossref
    5. Rashid Yarullin, Communications in Computer and Information Science, 1275, Mathematical Optimization Theory and Operations Research, 2020, 150  crossref
    6. 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
    7. Kalpana Dahiya, “Constrained integer fractional programming problem with box constraints”, SeMA, 74:4 (2017), 441  crossref
    8. 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
    9. I Ya Zabotin, O N Shulgina, R S Yarullin, “A minimization method on the basis of embedding the feasible set and the epigraph”, IOP Conf. Ser.: Mater. Sci. Eng., 158 (2016), 012098  crossref
    10. 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
    11. I. Ya. Zabotin, R. S. Yarullin, “A cutting-plane method without inclusions of approximating sets for conditional minimization”, Lobachevskii J Math, 36:2 (2015), 132  crossref
    12. 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
    13. 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
    14. 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
    15. 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
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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