期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2009
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：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.
关键词：mixed integer programs, split rank, group relaxations.
