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.
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
\Bibitem{PopSka16}
\by L.~D.~Popov, V.~D.~Skarin
\paper Duality and correction of inconsistent constraints for improper linear programming problems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 3
\pages 200--211
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\crossref{https://doi.org/10.21538/0134-4889-2016-22-3-200-211}
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2017
\vol 299
\issue , suppl. 1
\pages 165--176
\crossref{https://doi.org/10.1134/S008154381709019X}
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https://www.mathnet.ru/eng/timm1336
https://www.mathnet.ru/eng/timm/v22/i3/p200
This publication is cited in the following 2 articles:
Vl. D. Mazurov, M. I. Poberii, M. Yu. Khachai, “Ural School of Pattern Recognition: Majoritarian Approach to Ensemble Learning”, Pattern Recognit. Image Anal., 33:4 (2023), 1458
F. P. Vasil'ev, M. M. Potapov, L. A. Artem'eva, “Extragradient method for correction of inconsistent linear programming problems”, Comput. Math. Math. Phys., 58:12 (2018), 1919–1925
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