In this paper we study the t-branch split cuts introduced by Li and Richard (2008). They presented a family of mixed-integer programs with n integer variables and a single continuous variable and conjectured that the convex hull of integer solutions for any n has unbounded rank with respect to (n-1)-branch split cuts. It was shown … Read more
We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined recently in another paper). We then extend this observation to show that crooked cross cuts give the convex hull of mixed-integer sets with more integer variables provided that … Read more
In this paper, we study the relationship between {\em 2D lattice-free cuts}, the family of cuts obtained by taking two-row relaxations of a mixed-integer program (MIP) and applying intersection cuts based on maximal lattice-free sets in $\R^2$, and various types of disjunctions. Recently, Li and Richard (2007) studied disjunctive cuts obtained from $t$-branch split disjunctions … Read more