Elementary Closures for Integer Programs

In integer programming, the elementary closure associated with a family of cuts is the convex set defined by the intersection of all the cuts in the family. In this paper, we compare the elementary closures arising from several classical families of cuts: three versions of Gomory's fractional cuts, three versions of Gomory's mixed integer cuts, two versions of intersection cuts and their strengthened forms, Chvátal cuts, MIR cuts, lift- and-project cuts without and with strengthening, two versions of disjunctive cuts, Sherali- Adams cuts and Lovász-Schrijver cuts with positive semi-definiteness constraints.