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Fixing variables in semidefinite relaxations

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Algorithms — ESA '97 (ESA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1284))

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Abstract

The standard technique of reduced cost fixing from linear programming is not trivially extensible to semidefinite relaxations as the corresponding Lagrange multipliers are usually not available. We pro pose a general technique for computing reasonable Lagrange multipliers to constraints which are not part of the problem description. Its specialization to the semidefinite {-1,1} relaxation of quadratic 0-1 programming yields an efficient routine for fixing variables. The routine offers the possibility to exploit problem structure. We extend the traditional bijective map between {0,1} and {-1,1} formulations to the constraints such that the dual variables remain the same and structural properties are preserved. In consequence the fixing routine can efficiently be applied to optimal solutions of the semidefinite {0,1} relaxation of constrained quadratic 0-1 programming, as well. We provide numerical results showing the efficacy of the approach.

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Authors and Affiliations

  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustrafle 7, D-14195, Berlin, Germany

    Christoph Heimberg

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  1. Christoph Heimberg
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Rainer Burkard Gerhard Woeginger

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© 1997 Springer-Verlag Berlin Heidelberg

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Heimberg, C. (1997). Fixing variables in semidefinite relaxations. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_20

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  • DOI: https://doi.org/10.1007/3-540-63397-9_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63397-6

  • Online ISBN: 978-3-540-69536-3

  • eBook Packages: Springer Book Archive

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