Combining semidefinite and polyhedral relaxations for integer programs

  • C. Helmberg
  • S. Poljak
  • F. Rendl
  • H. Wolkowicz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 920)


We present a general framework for designing semidefinite relaxations for constrained 0–1 quadratic programming and show how valid inequalities of the cut-polytope can be used to strengthen these relaxations. As examples we improve the ϑ-function and give a semidefinite relaxation for the quadratic knapsack problem. The practical value of this approach is supported by numerical experiments which make use of the recent development of efficient interior point codes for semidefinite programming.

Key words

integer linear programming semidefinite programming quadratic 0–1 optimization interior point methods 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • C. Helmberg
    • 1
  • S. Poljak
    • 2
  • F. Rendl
    • 1
  • H. Wolkowicz
    • 3
  1. 1.Institut für MathematikTechnische Universität GrazGrazAustria
  2. 2.Institut für Mathematik und InformatikUniversität PassauPassauGermany
  3. 3.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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