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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 7, Pages 1151–1157 (Mi zvmmf275)  

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

Refinement of Lagrangian bounds in optimization problems

I. S. Litvinchev

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

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.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:7, 1101–1107

Bibliographic databases:

UDC: 519.658.4
Received: 01.09.2006
Revised: 09.01.2007

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
\Bibitem{Lit07}
\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://www.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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    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. I. S. Litvinchev, S. Rangel, “Comparison of Lagrangian bounds for one class of generalized assignment problems”, Comput. Math. Math. Phys., 48:5 (2008), 739–746  mathnet  crossref  mathscinet  zmath  isi
    2. J. Comput. Systems Sci. Internat., 48:3 (2009), 363–369  crossref  mathscinet  zmath  isi  elib  scopus
    3. Litvinchev I., Mata M., Rangel S., Saucedo J., “Lagrangian heuristic for a class of the generalized assignment problems”, Computers & Mathematics With Applications, 60:4 (2010), 1115–1123  crossref  mathscinet  zmath  isi  scopus
    4. Velarde Cantu J.M., Bueno Solano A., Lagarda Leyva E.A., Lopez Acosta M., “Optimization of Territories and Transport Routes For Hazardous Materials in a Distribution Network”, J. Ind. Eng. Manag.-JIEM, 10:4, SI (2017), 604–622  crossref  mathscinet  isi  scopus
    5. Litvinchev I.S., Cedillo G., Velarde M., “Integrating Territory Design and Routing Problems”, J. Comput. Syst. Sci. Int., 56:6 (2017), 969–974  crossref  mathscinet  zmath  isi  scopus
    6. Litvinchev I., Mata M., Saucedo J., Rangel S., “Improved Lagrangian Bounds and Heuristics For the Generalized Assignment Problem”, J. Comput. Syst. Sci. Int., 56:5 (2017), 803–809  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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