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Avtomat. i Telemekh., 2015, Issue 11, Pages 76–88 (Mi at14305)  

This article is cited in 4 scientific papers (total in 4 papers)

System Analysis and Operations Research

Cutting-plane method based on epigraph approximation with discarding the cutting planes

I. Ya. Zabotin, R. S. Yarullin

Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: Propose a method for solving a mathematical programming problem from the class of cutting methods. In our method, on each step the epigraph of the objective function is embedded into a specifically constructed polyhedral set, and on this set an auxiliary linear function is minimized in order to construct the iteration point. Proposed method does not require that each approximation set is embedded in the previous ones. This feature lets us periodically discard additional constraints that form the approximation sets obtained during the solution process. Prove the method's convergence and discuss possible implementations.

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English version:
Automation and Remote Control, 2015, 76:11, 1966–1975

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Presented by the member of Editorial Board: . . 

Received: 18.01.2015

Citation: I. Ya. Zabotin, R. S. Yarullin, “Cutting-plane method based on epigraph approximation with discarding the cutting planes”, Avtomat. i Telemekh., 2015, no. 11, 76–88; Autom. Remote Control, 76:11 (2015), 1966–1975

Citation in format AMSBIB
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\by I.~Ya.~Zabotin, R.~S.~Yarullin
\paper Cutting-plane method based on epigraph approximation with discarding the cutting planes
\jour Avtomat. i Telemekh.
\yr 2015
\issue 11
\pages 76--88
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\jour Autom. Remote Control
\yr 2015
\vol 76
\issue 11
\pages 1966--1975
\crossref{https://doi.org/10.1134/S0005117915110065}
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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, K. E. Kazaeva, “One cutting plane algorithm using auxiliary functions”, 11Th International Conference on Mesh Methods For Boundry-Value Problems and Applications, IOP Conference Series-Materials Science and Engineering, 158, IOP Publishing Ltd, 2016, UNSP 012097  crossref  isi  scopus
    2. I. Zabotin, K. Kazaeva, “Cutting-plane method with embedding of epigraphs of auxiliary functions”, Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V. F. Demyanov, ed. L. Polyakova, IEEE, 2017, 365–368  isi
    3. R. Zeng, “Analytic center cutting plane methods for variational inequalities over convex bodies”, J. Inequal. Appl., 2018, 87  crossref  mathscinet  zmath  isi  scopus
    4. I. Ya. Zabotin, K. E. Kazaeva, “Variant metoda shtrafov s approksimatsiei nadgrafikov vspomogatelnykh funktsii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2019, 263–273  mathnet  crossref  elib
  • Avtomatika i Telemekhanika
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