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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 3, Pages 279–291 (Mi timm1219)  
This article is cited in 3 scientific papers (total in 3 papers)

Lexicographic regularization and duality for improper linear programming problems

L. D. Popovab, V. D. Skarinab

a Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (207 kB) Citations (3)
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Abstract: A new approach to the optimal lexicographic correction of improper linear programming problems is proposed. The approach is based on the multistep regularization of the classical Lagrange function with respect to primal and dual variables simultaneously. The regularized function can be used as a basis for generating new duality schemes for problems of this kind. Theorems on the convergence and numerical stability of the method are presented, and an informal interpretation of the obtained generalized solution is given.
Keywords: linear programming, duality, improper problems, generalized solutions, regularization, penalty methods.
Received: 11.03.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 295, Issue 1, Pages 131–144
DOI: https://doi.org/10.1134/S0081543816090145
Bibliographic databases:
Document Type: Article
UDC: 519.658.4
Language: Russian
Citation: L. D. Popov, V. D. Skarin, “Lexicographic regularization and duality for improper linear programming problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 3, 2015, 279–291; Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 131–144
Citation in format AMSBIB
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\by L.~D.~Popov, V.~D.~Skarin
\paper Lexicographic regularization and duality for improper linear programming problems
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\vol 21
\issue 3
\pages 279--291
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 295
\issue , suppl. 1
\pages 131--144
\crossref{https://doi.org/10.1134/S0081543816090145}
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  • https://www.mathnet.ru/eng/timm/v21/i3/p279
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
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