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 f amily. In this paper, we compare the elementary closures arising from sever al 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, Chvatal cuts, MIR cuts, lift-and-projec t cuts without and with strengthening, two versions of disjunctive cuts, Sh erali-Adams cuts and Lovasz-Schrijver cuts with positive semi-definiteness constraints. (C) 2001 Published by Elsevier Science B.V.