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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 4, Pages 99–103 (Mi ivm7294)  
This article is cited in 7 scientific papers (total in 7 papers)

Brief communications

Connection of some bilevel and nonlinear optimization problems

A. V. Malyshev, A. S. Strekalovsky

Institute of Dynamic Systems and Control Theory of Siberian Branch of Russian Acedemy of Sciences, Irkutsk, Russia
Full-text PDF (162 kB) Citations (7)
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Abstract: In this paper we reduce a quadratic-linear bilevel optimization problem with a guaranteed solution to a family of bilevel problems in the optimistic statement. Then we reduce the obtained bilevel problems to nonconvex one-level optimization problems for solving the latter by nonconvex optimization methods.
Keywords: bilevel optimization problems, guaranteed (pessimistic) solution, nonconvex optimization problems.
Presented by the member of Editorial Board: Ya. I. Zabotin
Received: 21.10.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 4, Pages 83–86
DOI: https://doi.org/10.3103/S1066369X11040104
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
Citation: A. V. Malyshev, A. S. Strekalovsky, “Connection of some bilevel and nonlinear optimization problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 4, 99–103; Russian Math. (Iz. VUZ), 55:4 (2011), 83–86
Citation in format AMSBIB
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\by A.~V.~Malyshev, A.~S.~Strekalovsky
\paper Connection of some bilevel and nonlinear optimization problems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 4
\pages 99--103
\mathnet{http://mi.mathnet.ru/ivm7294}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2919800}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 4
\pages 83--86
\crossref{https://doi.org/10.3103/S1066369X11040104}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958724207}
Linking options:
  • https://www.mathnet.ru/eng/ivm7294
  • https://www.mathnet.ru/eng/ivm/y2011/i4/p99
    • This publication is cited in the following 7 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. A. V. Orlov, A. V. Malyshev, “The test problem generation for quadratic-linear pessimistic bilevel optimization”, Num. Anal. Appl., 7:3 (2014), 204–214  mathnet  crossref  mathscinet
    3. Alexander S. Strekalovsky, Optimization in Science and Engineering, 2014, 465  crossref
    4. Wiesemann W., Tsoukalas A., Kleniati P.-M., Rustem B., “Pessimistic Bilevel Optimization”, SIAM J. Optim., 23:1 (2013), 353–380  crossref  mathscinet  zmath  isi  elib
    5. Aliawdin P. Urbanska K., “Limit Analysis of Geometrically Hardening Rod Systems Using Bilevel Programming”, Modern Building Materials, Structures and Techniques, Procedia Engineering, 57, ed. Juozapaitis A. Vainiunas P. Zavadskas E., Elsevier Science BV, 2013, 89–98  crossref  isi
    6. 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
    7. A. V. Malyshev, A. S. Strekalovskii, “Globalnyi poisk garantirovannykh reshenii v kvadratichno-lineinykh zadachakh dvukhurovnevoi optimizatsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:1 (2011), 73–82  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:492
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    References:75
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