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Semidefinite Relaxations for Integer Programming

In: 50 Years of Integer Programming 1958-2008

Author

Listed:
  • Franz Rendl

    (Department of Mathematics, Alpen-Adria Universität)

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.

Suggested Citation

  • Franz Rendl, 2010. "Semidefinite Relaxations for Integer Programming," Springer Books, in: Michael Jünger & Thomas M. Liebling & Denis Naddef & George L. Nemhauser & William R. Pulleyblank & (ed.), 50 Years of Integer Programming 1958-2008, chapter 0, pages 687-726, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-68279-0_18
    DOI: 10.1007/978-3-540-68279-0_18
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