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

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

2012-04-08

arxiv.org/abs/1204.1715v1

Mathematics

Optimization and Control

Scientific paper

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.

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