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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 7, Pages 1151–1157 (Mi zvmmf275)  
This article is cited in 21 scientific papers (total in 21 papers)

Refinement of Lagrangian bounds in optimization problems

I. S. Litvinchev

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
Full-text PDF (984 kB) Citations (21)
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Abstract: Lagrangian constraint relaxation and the corresponding bounds for the optimal value of an original optimization problem are examined. Techniques for the refinement of the classical Lagrangian bounds are investigated in the case where the complementary slackness conditions are not fulfilled because either the original formulation is nonconvex or the Lagrange multipliers are nonoptimal. Examples are given of integer and convex problems for which the modified bounds improve the classical Lagrangian bounds.
Key words: Lagrangian bounds in optimization problems, refinement of Lagrangian bounds, optimization problems.
Received: 01.09.2006
Revised: 09.01.2007
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 7, Pages 1101–1107
DOI: https://doi.org/10.1134/S0965542507070032
Bibliographic databases:
Document Type: Article
UDC: 519.658.4
Language: Russian
Citation: I. S. Litvinchev, “Refinement of Lagrangian bounds in optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 47:7 (2007), 1151–1157; Comput. Math. Math. Phys., 47:7 (2007), 1101–1107
Citation in format AMSBIB
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\by I.~S.~Litvinchev
\paper Refinement of Lagrangian bounds in optimization problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 7
\pages 1151--1157
\mathnet{http://mi.mathnet.ru/zvmmf275}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2376657}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 7
\pages 1101--1107
\crossref{https://doi.org/10.1134/S0965542507070032}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547653773}
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    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Abstract page:340
    Full-text PDF :254
    References:44
    First page:1
     
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