Theory of linear and integer programming
Theory of linear and integer programming
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
Split closure and intersection cuts
Mathematical Programming: Series A and B
Inequalities from Two Rows of a Simplex Tableau
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
An Analysis of Mixed Integer Linear Sets Based on Lattice Point Free Convex Sets
Mathematics of Operations Research
MIR closures of polyhedral sets
Mathematical Programming: Series A and B
Maximal Lattice-Free Polyhedra: Finiteness and an Explicit Description in Dimension Three
Mathematics of Operations Research
A constructive characterization of the split closure of a mixed integer linear program
Operations Research Letters
The split closure of a strictly convex body
Operations Research Letters
Cook, Kannan and Schrijver's example revisited
Discrete Optimization
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Split cuts form a well-known class of valid inequalities for mixed-integer programming problems (MIP). Cook et al. (1990) showed that the split closure of a rational polyhedron P is again a polyhedron. In this paper, we extend this result from a single rational polyhedron to the union of a finite number of rational polyhedra. We also show how this result can be used to prove that some generalizations of split cuts, namely cross cuts, also yield closures that are rational polyhedra.