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Sib. Zh. Vychisl. Mat., 2010, Volume 13, Number 2, Pages 201–212 (Mi sjvm277)  

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.

Full text: PDF file (242 kB)
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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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    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. 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  mathnet  elib
    2. Malyshev A.V., “Algoritm globalnogo poiska garantirovannykh reshenii kvadratichno-lineinoi dvukhurovnevoi zadachi i ego testirovanie”, Vestnik buryatskogo gosudarstvennogo universiteta, 2012, no. 9, 17–21  elib
    3. 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
    4. 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  crossref  isi  scopus
    5. S. V. Ivanov, “Bilevel stochastic linear programming problems with quantile criterion”, Autom. Remote Control, 75:1 (2014), 107–118  mathnet  crossref  isi
    6. 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
    7. 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
    8. 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
    9. 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  crossref  mathscinet  zmath  isi  scopus
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