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50 Years of Integer Programming 1958-2008 pp 687–726Cite as

Semidefinite Relaxations for Integer Programming

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Abstract

We survey some recent developments in the area of semidefinite optimization applied to integer programming. After recalling some generic modeling techniques to obtain semidefinite relaxations for NP-hard problems, we look at the theoretical power of semidefinite optimization in the context of the Max-Cut and the Coloring Problem. In the second part, we consider algorithmic questions related to semidefinite optimization, and point to some recent ideas to handle large scale problems. The survey is concluded with some more advanced modeling techniques, based on matrix relaxations leading to copositive matrices.

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Authors and Affiliations

  1. Department of Mathematics, Alpen-Adria Universität, Klagenfurt, Austria

    Franz Rendl

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  1. Franz Rendl
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Correspondence to Franz Rendl .

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Editors and Affiliations

  1. Inst. Informatik, Universität Köln, Pohligstr. 1, Köln, 50969, Germany

    Michael Jünger

  2. Fac. Sciences de Base (FSB), Ecole Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland

    Thomas M. Liebling

  3. Ensimag, Institut Polytechnique de Grenoble, avenue Félix Viallet 46, Grenoble CX 1, 38031, France

    Denis Naddef

  4. School of Industrial &, Georgia Institute of Technology, Ferst Drive NW., 765, Atlanta, 30332-0205, USA

    George L. Nemhauser

  5. IBM Corporation, Route 100 294, Somers, 10589, USA

    William R. Pulleyblank

  6. Inst. Informatik, Universität Heidelberg, Im Neuenheimer Feld 326, Heidelberg, 69120, Germany

    Gerhard Reinelt

  7. ed Informatica, CNR - Ist. Analisi dei Sistemi, Viale Manzoni 30, Roma, 00185, Italy

    Giovanni Rinaldi

  8. Center for Operations Reserach &, Université Catholique de Louvain, voie du Roman Pays 34, Leuven, 1348, Belgium

    Laurence A. Wolsey

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Rendl, F. (2010). Semidefinite Relaxations for Integer Programming. In: Jünger, M., et al. 50 Years of Integer Programming 1958-2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68279-0_18

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