Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2013, Volume 155, Book 2, Pages 54–64 (Mi uzku1197)  

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

A Cutting-Plane Method with Updating of Approximating Sets and Estimates of the Solution Accuracy

I. Ya. Zabotin, R. S. Yarullin

Kazan (Volga Region) Federal University

Abstract: We propose a cutting-plane method for solving a mathematical programming problem. A sequence of approximations is constructed using the technique of partial immersion of the admissible set in the approximating polyhedral sets. The developed method does not require the inclusion of each of the approximating sets in the previous one. This peculiarity makes it possible to periodically drop any additional planes which occur in the problem-solving process. We describe the features of the method, prove its convergence, and obtain estimates of the solution accuracy.

Keywords: approximating set, cutting plane, estimates of solution accuracy, sequence of approximations, convergence, conditional minimization.

Full text: PDF file (266 kB)
References: PDF file   HTML file
UDC: 519.853
Received: 12.04.2013

Citation: I. Ya. Zabotin, R. S. Yarullin, “A Cutting-Plane Method with Updating of Approximating Sets and Estimates of the Solution Accuracy”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 155, no. 2, Kazan University, Kazan, 2013, 54–64

Citation in format AMSBIB
\Bibitem{ZabYar13}
\by I.~Ya.~Zabotin, R.~S.~Yarullin
\paper A Cutting-Plane Method with Updating of Approximating Sets and Estimates of the Solution Accuracy
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2013
\vol 155
\issue 2
\pages 54--64
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1197}


Linking options:
  • http://mi.mathnet.ru/eng/uzku1197
  • http://mi.mathnet.ru/eng/uzku/v155/i2/p54

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “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
    2. 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
    3. 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
  • Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
    Number of views:
    This page:247
    Full text:145
    References:125

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021