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This article is cited in 9 scientific papers (total in 9 papers)
Numerical solution of a class of bilevel programming problems
A. S. Strekalovsky, A. V. Orlov, A. V. Malyshev
Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
Abstract:
The quadratic-linear bilevel programming problem is considered. Its optimistic statement is reduced to a series of non-convex mathematical programming problems. An approximate algorithm of the global search in the problems obtained is proposed. Numerical solutions of randomly generated test problems are given and analyzed.
Key words:
bilevel programming, optimistic solution, non-convex optimization problems, global search, computational simulation.
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English version:
Numerical Analysis and Applications, 2010, 3:2, 165–173
UDC:
519.853.4
Received: 25.06.2009
Citation:
A. S. Strekalovsky, A. V. Orlov, A. V. Malyshev, “Numerical solution of a class of bilevel programming problems”, Sib. Zh. Vychisl. Mat., 13:2 (2010), 201–212; Num. Anal. Appl., 3:2 (2010), 165–173
Citation in format AMSBIB
\Bibitem{StrOrlMal10}
\by A.~S.~Strekalovsky, A.~V.~Orlov, A.~V.~Malyshev
\paper Numerical solution of a~class of bilevel programming problems
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 2
\pages 201--212
\mathnet{http://mi.mathnet.ru/sjvm277}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 2
\pages 165--173
\crossref{https://doi.org/10.1134/S1995423910020059}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953530160}
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http://mi.mathnet.ru/eng/sjvm277 http://mi.mathnet.ru/eng/sjvm/v13/i2/p201
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Gruzdeva T.V., Strekalovskii A.S., Orlov A.V., Druzhinina O.V., “Negladkie zadachi minimizatsii raznosti dvukh vypuklykh funktsii”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 12:1 (2011), 384–396
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Malyshev A.V., “Algoritm globalnogo poiska garantirovannykh reshenii kvadratichno-lineinoi dvukhurovnevoi zadachi i ego testirovanie”, Vestnik buryatskogo gosudarstvennogo universiteta, 2012, no. 9, 17–21
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A. V. Orlov, “Globalnyi poisk optimisticheskikh reshenii v dvukhurovnevoi zadache optimalnogo vybora tarifov telekommunikatsionnym operatorom”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:1 (2013), 57–71
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Aliawdin P., Urbanska K., “Limit Analysis of Geometrically Hardening Rod Systems Using Bilevel Programming”, Modern Building Materials, Structures and Techniques, Procedia Engineering, 57, eds. Juozapaitis A., Vainiunas P., Zavadskas E., Elsevier Science BV, 2013, 89–98
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S. V. Ivanov, “Bilevel stochastic linear programming problems with quantile criterion”, Autom. Remote Control, 75:1 (2014), 107–118
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A. V. Orlov, “Chislennyi poisk globalnykh reshenii v zadachakh nesimmetrichnoi bilineinoi otdelimosti”, Diskretn. analiz i issled. oper., 22:1 (2015), 64–85
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A. V. Orlov, S. Batbileg, “Oligopolisticheskii bankovskii sektor Mongolii i polimatrichnye igry trekh lits”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 11 (2015), 80–95
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Orlov A.V., Strekalovsky A.S., Batbileg S., “on Computational Search For Nash Equilibrium in Hexamatrix Games”, Optim. Lett., 10:2 (2016), 369–381
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Pineda S., Bylling H., Morales J.M., “Efficiently Solving Linear Bilevel Programming Problems Using Off-the-Shelf Optimization Software”, Optim. Eng., 19:1 (2018), 187–211
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