30 citations · 73 across the 10 of their papers we have counts for
7 papers · 1 filter
Characterization of the Split Closure via Geometric Lifting
Amitabh Basu, Marco Molinaro
We analyze split cuts from the perspective of cut generating functions via geometric lifting. We show that -cuts, a natural higher-dimensional generalization of the -cuts of…
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…
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…
Mixed-integer linear representability, disjunctions, and variable elimination
Amitabh Basu, Kipp Martin, Christopher Ryan +1
Jeroslow and Lowe gave an exact geometric characterization of subsets of that are projections of mixed-integer linear sets, a.k.a MILP-representable sets. We give an…
Optimality certificates for convex minimization and Helly numbers
Amitabh Basu, Michele Conforti, Gérard Cornuéjols +2
We consider the problem of minimizing a convex function over a subset of R^n that is not necessarily convex (minimization of a convex function over the integer points in a polytope…
Lifting properties of maximal lattice-free polyhedra
Gennadiy Averkov, Amitabh Basu
We study the uniqueness of minimal liftings of cut-generating functions obtained from maximal lattice-free polyhedra. We prove a basic invariance property of unique minimal lifting…