Abstract:
A method for solving the following inverse linear programming (LP) problem is proposed. For a given LP problem and one of its feasible vectors, it is required to adjust the objective function vector as little as possible so that the given vector becomes optimal. The closeness of vectors is estimated by means of the Euclidean vector norm. The inverse LP problem is reduced to a problem of unconstrained minimization for a convex piecewise quadratic function. This minimization problem is solved by means of the generalized Newton method.
Keywords:
linear programming, inverse linear programming problem, duality, unconstrained optimization, generalized newton method.
Citation:
G. A. Amirkhanova, A. I. Golikov, Yu. G. Evtushenko, “On an inverse linear programming problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 3, 2015, 13–19; Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 21–27
\Bibitem{AmiGolEvt15}
\by G.~A.~Amirkhanova, A.~I.~Golikov, Yu.~G.~Evtushenko
\paper On an inverse linear programming problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 3
\pages 13--19
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 295
\issue , suppl. 1
\pages 21--27
\crossref{https://doi.org/10.1134/S0081543816090030}
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Linking options:
https://www.mathnet.ru/eng/timm1193
https://www.mathnet.ru/eng/timm/v21/i3/p13
This publication is cited in the following 3 articles:
András Kovács, “Inverse optimization approach to the identification of electricity consumer models”, Cent Eur J Oper Res, 29:2 (2021), 521
Vladimir Erokhin, Sergey Sotnikov, Andrey Kadochnikov, Alexey Vaganov, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 283
V. V. Volkov, V. I. Erokhin, A. S. Krasnikov, A. V. Razumov, M. N. Khvostov, “Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems”, Comput. Math. Math. Phys., 57:11 (2017), 1757–1770