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Sibirskii Zhurnal Industrial'noi Matematiki, 2018, Volume 21, Number 1, Pages 11–20
DOI: https://doi.org/10.17377/sibjim.2018.21.102
(Mi sjim985)
 

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

Interior point algorithms in linear optimization

V. I. Zorkaltsev, I. V. Mokryi

Melentiev Energy Systems Institute SB RAS, 130 Lermontov str., 664033 Irkutsk
Full-text PDF (227 kB) Citations (3)
References:
Abstract: This is a survey of the results concerning the development and study of the interior point algorithms. Some families of the direct and dual algorithms are considered. These algorithms entering the domain of feasible solutions take into account the objective function, which makes it possible to obtain the first feasible solution close to the optimal solution. The main results on the theoretical justification of algorithms are given. Recommendations are proposed concerning the advantages of individual variants of algorithms on the basis of the obtained theoretical results, available experimental studies, and experience of using algorithms in the models of energy engineering. Some numerically efficient version of the polynomial optimization algorithm in the cone of the central path is also presented.
Keywords: interior point method, relative interior, central path, linear programming.
Funding agency Grant number
Russian Foundation for Basic Research 15-07-07412а
Received: 14.04.2017
English version:
Journal of Applied and Industrial Mathematics, 2018, Volume 12, Issue 1, Pages 191–199
DOI: https://doi.org/10.1134/S1990478918010179
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: V. I. Zorkaltsev, I. V. Mokryi, “Interior point algorithms in linear optimization”, Sib. Zh. Ind. Mat., 21:1 (2018), 11–20; J. Appl. Industr. Math., 12:1 (2018), 191–199
Citation in format AMSBIB
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\transl
\jour J. Appl. Industr. Math.
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Linking options:
  • https://www.mathnet.ru/eng/sjim985
  • https://www.mathnet.ru/eng/sjim/v21/i1/p11
  • This publication is cited in the following 3 articles:
    1. N. A. Olkhovsky, L. B. Sokolinsky, “Surface Movement Method for Linear Programming”, Lobachevskii J Math, 45:10 (2024), 5172  crossref
    2. W. Liu, L. Yang, B. Yu, “A lifting-penalty method for quadratic programming with a quadratic matrix inequality constraint”, Mathematics, 8:2 (2020), 153  crossref  isi  scopus
    3. Aleksandr Domyshev, Denis Sidorov, Daniil Panasetsky, Yonghui Sun, Ping Ju, Feng Wu, 2018 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2), 2018, 1  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
    Statistics & downloads:
    Abstract page:367
    Full-text PDF :223
    References:43
    First page:6
     
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