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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, Volume 161, Book 2, Pages 263–273
DOI: https://doi.org/10.26907/2541-7746.2019.2.263-273
(Mi uzku1516)
 

This article is cited in 2 scientific papers (total in 2 papers)

A version of the penalty method with approximation of the epigraphs of auxiliary functions

I. Ya. Zabotin, K. E. Kazaeva

Kazan Federal University, Kazan, 420008 Russia
Full-text PDF (594 kB) Citations (2)
References:
Abstract: A method for solving the convex programming problem, which is ideologically close to the known methods of external penalties, was proposed. The method uses auxiliary functions that are built on the general form of the penalty functions. In order to find approximations, the epigraphs of these auxiliary functions, as well as the original problem's domain of constraints, were immersed in certain polyhedral sets. In this regard, the problems of finding the iterative points are the linear programming problems, in which the constraints are the sets that approximate the epigraphs and a polyhedron containing an admissible set. The approximating sets were constructed using the traditional cutting of iterative points by planes. The peculiarity of the method is that it enables a periodic update of the approximating sets by discarding the cutting planes. The convergence of the proposed method was proved. Its implementation was discussed.
Keywords: conditional minimization, iterative point, convergence, penalty function, epigraph, approximating set, cutting hyperplane.
Received: 11.03.2019
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
Citation: I. Ya. Zabotin, K. E. Kazaeva, “A version of the penalty method with approximation of the epigraphs of auxiliary functions”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 161, no. 2, Kazan University, Kazan, 2019, 263–273
Citation in format AMSBIB
\Bibitem{ZabKaz19}
\by I.~Ya.~Zabotin, K.~E.~Kazaeva
\paper A version of the penalty method with approximation of the epigraphs of auxiliary functions
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2019
\vol 161
\issue 2
\pages 263--273
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1516}
\crossref{https://doi.org/10.26907/2541-7746.2019.2.263-273}
\elib{https://elibrary.ru/item.asp?id=41296516}
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  • https://www.mathnet.ru/eng/uzku/v161/i2/p263
  • This publication is cited in the following 2 articles:
    1. Igor Zabotin, Oksana Shulgina, Rashid Yarullin, Lecture Notes in Computational Science and Engineering, 141, Mesh Methods for Boundary-Value Problems and Applications, 2022, 575  crossref
    2. Rashid Yarullin, Igor Zabotin, Communications in Computer and Information Science, 1661, Mathematical Optimization Theory and Operations Research: Recent Trends, 2022, 204  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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