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Approaches to Integer Programming pp 82–114Cite as

Lagrangean relaxation for integer programming

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Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 2))

Abstract

Taking a set of “complicating” constraints of a general mixed integer program up into the objective function in a Lagrangean fashion (with fixed multipliers) yields a “Lagrangean relaxation” of the original program. This paper gives a systematic development of this simple bounding construct as a means of exploiting special problem structure. A general theory is developed and special emphasis is given to the application of Lagrangean relaxation in the context of LP-based branch-and-bound.

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Authors and Affiliations

  1. University of California, Los Angeles, Calif., USA

    A. M. Geoffrion

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  1. A. M. Geoffrion
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M. L. Balinski

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© 1974 The Mathematical Programming Society

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Geoffrion, A.M. (1974). Lagrangean relaxation for integer programming. In: Balinski, M.L. (eds) Approaches to Integer Programming. Mathematical Programming Studies, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120690

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  • DOI: https://doi.org/10.1007/BFb0120690

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00739-2

  • Online ISBN: 978-3-642-00740-8

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