77 citations · 281 across the 10 of their papers we have counts for
7 papers · 2 filters
Unique lifting of integer variables in minimal inequalities
Amitabh Basu, Manoel Campelo, Michele Conforti +2
This paper contributes to the theory of cutting planes for mixed integer linear programs (MILPs). Minimal valid inequalities are well understood for a relaxation of an MILP in tabl…
A Counterexample to a Conjecture of Gomory and Johnson
Amitabh Basu, Michele Conforti, Gerard Cornuejols +1
In Mathematical Programming 2003, Gomory and Johnson conjecture that the facets of the infinite group problem are always generated by piecewise linear functions. In this paper we g…
Intersection Cuts with Infinite Split Rank
Amitabh Basu, Gerard Cornuejols, Francois Margot
We consider mixed integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, D…
Experiments with two-row cuts from degenerate tableaux
Amitabh Basu, Pierre Bonami, Gerard Cornuejols +1
There has been a recent interest in cutting planes generated from two or more rows of the optimal simplex tableau. One can construct examples of integer programs for which a single…
Maximal lattice-free convex sets in linear subspaces
Amitabh Basu, Michele Conforti, Gerard Cornuejols +1
We consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal lattice-free convex sets in an affine subspace. We also…
Minimal inequalities for an infinite relaxation of integer programs
Amitabh Basu, Michele Conforti, Gerard Cornuejols +1
We show that maximal -free convex sets are polyhedra when is the set of integral points in some rational polyhedron of . This result extends a theorem of Lovás…