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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 3, Pages 200–211
DOI: https://doi.org/10.21538/0134-4889-2016-22-3-200-211 (Mi timm1336) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Duality and correction of inconsistent constraints for improper linear programming problems

L. D. Popovab, V. D. Skarinba

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (193 kB) Citations (2)
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DOI: https://doi.org/10.21538/0134-4889-2016-22-3-200-211
Abstract: We continue the study of approximation properties of alternative duality schemes for improper problems of linear programming. The schemes are based on the use of the classical Lagrange function regularized simultaneously in direct and dual variables. The results on the connection of its saddle points with the lexicographic correction of the right-hand sides of constraints in improper problems of the first and second kind are transferred to a more general type of improperness. Convergence theorems are presented and an informal interpretation is given for the obtained generalized solution.
Keywords: linear programming, duality, improper problems, generalized solutions, regularization, penalty methods.
Funding agency Grant number
Russian Science Foundation 14-11-00109
Received: 19.02.2016
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 299, Issue 1, Pages 165–176
DOI: https://doi.org/10.1134/S008154381709019X
Bibliographic databases:
Document Type: Article
UDC: 519.658.4
MSC: 90C05, 90C46
Language: Russian
Citation: L. D. Popov, V. D. Skarin, “Duality and correction of inconsistent constraints for improper linear programming problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 3, 2016, 200–211; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 165–176
Citation in format AMSBIB
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