منابع مشابه
Intersection Cuts with Infinite Split Rank
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, Dey and Louveaux characterized the intersection cuts that have infinite split rank. We show that, for any number of integer variables, the split rank of an intersection cut generated from a rational lattice-free polyto...
متن کاملA note on the split rank of intersection cuts
In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that dlog2(l)e is a lower bound on the split rank of the int...
متن کاملA Note on Split Rank of Intersection Cuts
In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that dlog2(l)e is a lower bound on the split rank of the int...
متن کاملSplit Closure and Intersection Cuts
In the seventies, Balas introduced intersection cuts for a Mixed Integer Linear Program (MILP), and showed that these cuts can be obtained by a closed form formula from a basis of the standard linear programming relaxation. In the early nineties, Cook, Kannan and Schrijver introduced the split closure of an MILP, and showed that the split closure is a polyhedron. In this paper, we show that the...
متن کاملComputing with Multi-Row Intersection Cuts
Cutting planes are one of the main techniques currently used to solve large-scale MixedInteger Linear Programming (MIP) models. Many important cuts used in practice, such as Gomory Mixed-Integer (GMI) cuts, are obtained by solving the linear relaxation of the MIP, extracting a single row of the simplex tableau, then applying integrality arguments to it. A natural extension, which has received r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2012
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.1110.0522