English

Improved theoretical guarantees regarding a class of two-row cutting planes

Optimization and Control 2012-04-10 v1 Discrete Mathematics Combinatorics

Abstract

The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for the approximation of the RCP, purely by minimal valid inequalities from maximal lattice-free quadrilaterals, from 2 to 1.71. We generalize the tightest known lower bound of 1.125 for the approximation of the RCP, purely by minimal valid inequalities from maximal lattice-free triangles, to an infinite subclass of quadrilaterals.

Keywords

Cite

@article{arxiv.1204.1715,
  title  = {Improved theoretical guarantees regarding a class of two-row cutting planes},
  author = {Yogesh P. Awate},
  journal= {arXiv preprint arXiv:1204.1715},
  year   = {2012}
}