Exploiting symmetry in integer convex optimization using core points

@article{Herr2013ExploitingSI,
  title={Exploiting symmetry in integer convex optimization using core points},
  author={Katrin Herr and Thomas Rehn and Achill Sch{\"u}rmann},
  journal={Oper. Res. Lett.},
  year={2013},
  volume={41},
  pages={298-304}
}
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. To decompose such problems, we introduce the new concept of core points, i.e., integral points whose orbit polytopes are lattice-free. For symmetric integer linear programs, we describe two algorithms based on this decomposition. Using a characterization of core points for direct products of symmetric groups, we show that prototype implementations can compete with state-of… CONTINUE READING