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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2010, Volume 13, Number 2, Pages 201–212 (Mi sjvm277)  
This article is cited in 13 scientific papers (total in 13 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
Full-text PDF (242 kB) Citations (13)
References:
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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.
Received: 25.06.2009
English version:
Numerical Analysis and Applications, 2010, Volume 3, Issue 2, Pages 165–173
DOI: https://doi.org/10.1134/S1995423910020059
Bibliographic databases:
Document Type: Article
UDC: 519.853.4
Language: Russian
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
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\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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  • https://www.mathnet.ru/eng/sjvm277
  • https://www.mathnet.ru/eng/sjvm/v13/i2/p201
    • This publication is cited in the following 13 articles:
    1. Piotr Alawdin, Krystyna Urbańska, “Limit Analysis of Geometrically Hardening Composite Steel-Concrete Systems / Stany Graniczne Geometrycznie Wzmacniających Siȩ Konstrukcji Zespolonych”, Civil and Environmental Engineering Reports, 16:1 (2023), 5  crossref
    2. Stephan Dempe, Springer Optimization and Its Applications, 161, Bilevel Optimization, 2020, 581  crossref
    3. 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
    4. Andrei V. Orlov, Springer Proceedings in Mathematics & Statistics, 247, Computational Aspects and Applications in Large-Scale Networks, 2018, 57  crossref
    5. 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
    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. S. V. Ivanov, “Bilevel stochastic linear programming problems with quantile criterion”, Autom. Remote Control, 75:1 (2014), 107–118  mathnet  crossref  isi
    9. Alexander S. Strekalovsky, Optimization in Science and Engineering, 2014, 465  crossref
    10. 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
    11. 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
    12. Malyshev A.V., “Algoritm globalnogo poiska garantirovannykh reshenii kvadratichno-lineinoi dvukhurovnevoi zadachi i ego testirovanie”, Vestnik buryatskogo gosudarstvennogo universiteta, 2012, no. 9, 17–21 Algorithm of global search for guaranteed solutions to quadratic-linear bilevel problem and its testing  elib
    13. 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
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