Abstract:
A family of interior point algorithms for the linear programming problems is considered. In these algorithms, the entering into the domain of admissible solution of the original problem is represented as optimization process of the extended problem. This extension is realized by adding just one new variable. The main objective of the paper is to give a theoretical justification of the proposed procedure of entering into the feasible domain of the original problem, under the assumption of non-degeneracy of the extended problem. Particularly, we prove that given the constraints of the original problem being consistent, the procedure leads to a relative interior point of the feasible solutions domain.
Key words:
interior point algorithm, linear programming, techniques of arriving at the feasible solutions region.
Citation:
V. I. Zorkaltsev, “The search for admissible solutions by the interior point algorithms”, Sib. Zh. Vychisl. Mat., 19:3 (2016), 249–265; Num. Anal. Appl., 9:3 (2016), 191–206
\Bibitem{Zor16}
\by V.~I.~Zorkaltsev
\paper The search for admissible solutions by the interior point algorithms
\jour Sib. Zh. Vychisl. Mat.
\yr 2016
\vol 19
\issue 3
\pages 249--265
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\crossref{https://doi.org/10.15372/SJNM20160302}
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\jour Num. Anal. Appl.
\yr 2016
\vol 9
\issue 3
\pages 191--206
\crossref{https://doi.org/10.1134/S1995423916030022}
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Linking options:
https://www.mathnet.ru/eng/sjvm616
https://www.mathnet.ru/eng/sjvm/v19/i3/p249
This publication is cited in the following 1 articles:
P. Drag, K. Styczen, “A general optimization-based approach for thermal processes modeling”, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems (FEDCSIS), eds. M. Ganzha, L. Maciaszek, M. Paprzycki, IEEE, 2017, 1347–1352
Citation in format AMSBIB
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