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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 10, Pages 1715–1726 (Mi zvmmf4943)  

This article is cited in 6 scientific papers (total in 6 papers)

Numerical solution of a linear bilevel problem

T. V. Gruzdeva, E. G. Petrova

Institute of Dynamical Systems and Control Theory, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033 Russia

Abstract: The linear bilevel programming problem in the optimistic formulation is studied. It is reduced to an optimization problem with a nonconvex constraint in the form of a d.c. function (that is, the difference of two convex functions). For this problem, local and global search methods are developed. Numerical experiments performed for numerous specially generated problems, including large-scale ones, demonstrate the efficiency of the proposed approach.

Key words: linear bilevel problem, optimistic solution, problem with d.c. inequality, local search, global search, numerical experiment.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:10, 1631–1641

Bibliographic databases:

UDC: 519.626
Received: 05.02.2010
Revised: 13.05.2010

Citation: T. V. Gruzdeva, E. G. Petrova, “Numerical solution of a linear bilevel problem”, Zh. Vychisl. Mat. Mat. Fiz., 50:10 (2010), 1715–1726; Comput. Math. Math. Phys., 50:10 (2010), 1631–1641

Citation in format AMSBIB
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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. 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
    2. Orlov A.V., “Gibridnyi geneticheskii algoritm globalnogo poiska optimisticheskikh reshenii v zadachakh dvukhurovnevoi optimizatsii”, Vestnik Buryatskogo gosudarstvennogo universiteta, 2013, no. 9, 25–32  elib
    3. Orlov A.V., “Ob odnom podkhode k dvukhurovnevoi zadache formirovaniya gruzovykh zheleznodorozhnykh sostavov”, Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie, 2013, no. 4(40), 15–22  elib
    4. S. V. Ivanov, “Bilevel stochastic linear programming problems with quantile criterion”, Autom. Remote Control, 75:1 (2014), 107–118  mathnet  crossref  isi
    5. Kuo R.J., Lee Y.H., Zulvia F.E., Tien F.C., “Solving Bi-Level Linear Programming Problem Through Hybrid of Immune Genetic Algorithm and Particle Swarm Optimization Algorithm”, Appl. Math. Comput., 266 (2015), 1013–1026  crossref  mathscinet  isi  elib  scopus
    6. Orlov A., “A Nonconvex Optimization Approach to Quadratic Bilevel Problems”, Learning and Intelligent Optimization (Lion 11 2017), Lecture Notes in Computer Science, 10556, eds. Battiti R., Kvasov D., Sergeyev Y., Springer International Publishing Ag, 2017, 222–234  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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