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Generalized Lagrange Multipliers in Integer Programming

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  • Jeremy F. Shapiro

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

This paper combines the theory of generalized Lagrange multipliers with a reformulation of the integer-programming problem due to group theory. The use of multipliers enhances the algorithmic efficiency of group theory in a variety of ways. One particular application is the approximation of generalized Lagrange multipliers by generalized linear programming as suggested by Brooks and Geoffrion. This procedure is shown to be closely related to the cutting-plane method of Gomory.

Suggested Citation

  • Jeremy F. Shapiro, 1971. "Generalized Lagrange Multipliers in Integer Programming," Operations Research, INFORMS, vol. 19(1), pages 68-76, February.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:1:p:68-76
    DOI: 10.1287/opre.19.1.68
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    Cited by:

    1. Lorena, Luiz Antonio N. & Goncalves Narciso, Marcelo, 2002. "Using logical surrogate information in Lagrangean relaxation: An application to symmetric traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 138(3), pages 473-483, May.
    2. Saez, Jesus, 2000. "Solving linear programming relaxations associated with Lagrangean relaxations by Fenchel cutting planes," European Journal of Operational Research, Elsevier, vol. 121(3), pages 609-626, March.
    3. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    4. M T Ramos & J Sáez, 2005. "Solving capacitated facility location problems by Fenchel cutting planes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 297-306, March.
    5. P N Ram Kumar & T T Narendran, 2011. "On the usage of Lagrangean Relaxation for the convoy movement problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 722-728, April.

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