Split rank of triangle and quadrilateral inequalities
(2009)
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- Authors
- Abstract
- A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [2] and Cornu´ejols and Margot [13] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Through a result by Cook et al. [12], it is known that one particular class of facet- defining triangle inequality does not have a finite split rank. In this paper, we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank. The proof is constructive and given a facet-defining triangle or quadrilateral inequality we present an explicit sequence of split inequalities that can be used to generate it.
- Affiliations
Université de Liège Montefiore Institute
Citations
Dey, S., & Louveaux, Q. (2009). Split rank of triangle and quadrilateral inequalities (CORE Discussion Papers 2009/55). https://hdl.handle.net/2078.5/250314