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An Effective Branch-and-Bound Algorithm for Convex Quadratic Integer Programming

  • Christoph Buchheim
  • Alberto Caprara
  • Andrea Lodi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6080)

Abstract

We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the variables using suitably-defined lattice-free ellipsoids. Experiments show that our approach is very fast on both unconstrained problems and problems with box constraints. The main reason is that all expensive calculations can be done in a preprocessing phase, while a single node in the enumeration tree can be processed in linear time in the problem dimension.

Keywords

Integer Point Enumeration Tree Unconstrained Case Unconstrained Binary Quadratic Programming Close Vector Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christoph Buchheim
    • 1
    • 2
  • Alberto Caprara
    • 2
  • Andrea Lodi
    • 2
  1. 1.Fakultät für MathematikTechnische Universität DortmundDortmundGermany
  2. 2.DEISUniversità di BolognaBolognaItaly

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