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This article is cited in 7 scientific papers (total in 7 papers)
A local search for the quadratic-linear bilevel programming problem
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 non-convex mathematical programming problem with the quadratic-bilinear structure. An approximate algorithm of a local search in the problem obtained is proposed, proved and tested.
Key words:
bilevel programming, optimistic solution, non-convex optimization problems, local search, test problems generating, computational simulation.
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English version:
Numerical Analysis and Applications, 2010, 3:1, 59–70
UDC:
519.853.4
Received: 25.06.2009
Revised: 09.10.2009
Citation:
A. S. Strekalovsky, A. V. Orlov, A. V. Malyshev, “A local search for the quadratic-linear bilevel programming problem”, Sib. Zh. Vychisl. Mat., 13:1 (2010), 75–88; Num. Anal. Appl., 3:1 (2010), 59–70
Citation in format AMSBIB
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\by A.~S.~Strekalovsky, A.~V.~Orlov, A.~V.~Malyshev
\paper A local search for the quadratic-linear bilevel programming problem
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 1
\pages 75--88
\mathnet{http://mi.mathnet.ru/sjvm269}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 1
\pages 59--70
\crossref{https://doi.org/10.1134/S1995423910010076}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952222900}
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http://mi.mathnet.ru/eng/sjvm269 http://mi.mathnet.ru/eng/sjvm/v13/i1/p75
Citing articles on Google Scholar:
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Russian articles,
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This publication is cited in the following articles:
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A. S. Strekalovsky, A. V. Orlov, A. V. Malyshev, “Numerical solution of a class of bilevel programming problems”, Num. Anal. Appl., 3:2 (2010), 165–173
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T. V. Gruzdeva, E. G. Petrova, “Numerical solution of a linear bilevel problem”, Comput. Math. Math. Phys., 50:10 (2010), 1631–1641
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A. V. Malyshev, A. S. Strekalovsky, “Connection of some bilevel and nonlinear optimization problems”, Russian Math. (Iz. VUZ), 55:4 (2011), 83–86
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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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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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