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Sib. Zh. Vychisl. Mat., 2010, Volume 13, Number 1, Pages 75–88 (Mi sjvm269)  

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.

Full text: PDF file (259 kB)
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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
\Bibitem{StrOrlMal10}
\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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref
    2. T. V. Gruzdeva, E. G. Petrova, “Numerical solution of a linear bilevel problem”, Comput. Math. Math. Phys., 50:10 (2010), 1631–1641  mathnet  crossref  adsnasa  isi
    3. A. V. Malyshev, A. S. Strekalovsky, “Connection of some bilevel and nonlinear optimization problems”, Russian Math. (Iz. VUZ), 55:4 (2011), 83–86  mathnet  crossref  mathscinet
    4. 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  mathnet
    5. A. V. Orlov, “Chislennyi poisk globalnykh reshenii v zadachakh nesimmetrichnoi bilineinoi otdelimosti”, Diskretn. analiz i issled. oper., 22:1 (2015), 64–85  mathnet  crossref  mathscinet  elib
    6. A. V. Orlov, S. Batbileg, “Oligopolisticheskii bankovskii sektor Mongolii i polimatrichnye igry trekh lits”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 11 (2015), 80–95  mathnet
    7. Orlov A.V. Strekalovsky A.S. Batbileg S., “on Computational Search For Nash Equilibrium in Hexamatrix Games”, Optim. Lett., 10:2 (2016), 369–381  crossref  mathscinet  zmath  isi  elib  scopus
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