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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 1, Pages 231–237 (Mi timm1045)  
This article is cited in 2 scientific papers (total in 2 papers)

Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind

L. D. Popovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after the First President of Russia B. N. Yeltsin
Full-text PDF (146 kB) Citations (2)
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Abstract: A novel dual approach to the problem of optimal correction of first-kind improper linear programming problems with respect to their right-hand sides is proposed. It is based on the extension of the traditional Lagrangian by introducing additional regularization and barrier components. Convergence theorems are given for methods based on the augmented Lagrangian, an informal interpretation of the obtained generalized solution is suggested, and results of numerical experiments are presented.
Keywords: linear programming, improper problems, generalized solutions, barrier function method.
Received: 10.01.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 288, Issue 1, Pages 173–179
DOI: https://doi.org/10.1134/S0081543815020170
Bibliographic databases:
Document Type: Article
UDC: 519.658.4
Language: Russian
Citation: L. D. Popov, “Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 231–237; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 173–179
Citation in format AMSBIB
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\paper Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind
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\vol 20
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\pages 231--237
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Linking options:
  • https://www.mathnet.ru/eng/timm1045
  • https://www.mathnet.ru/eng/timm/v20/i1/p231
    • This publication is cited in the following 2 articles:
    1. L. D. Popov, “Interior Point Methods Adapted to Improper Linear Programs”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S116–S124  mathnet  crossref  crossref  isi  elib
    2. G. A. Amirkhanova, A. I. Golikov, Yu. G. Evtushenko, “On an inverse linear programming problem”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 21–27  mathnet  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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