Every Nontrivial Facet-Defining Inequality for the Corner Polyhedron is an Intersection Cut

نویسندگان

  • Michele Conforti
  • Gérard Cornuéjols
  • Giacomo Zambelli
چکیده

Intersection cuts were introduced by Balas and the corner polyhedron by Gomory. It is a classical result that intersection cuts are valid for the corner polyhedron. In this paper we show that, conversely every nontrivial facet-defining inequality for the corner polyhedron is an intersection cut.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Equivalence between intersection cuts and the corner polyhedron

Intersection cuts were introduced by Balas and the corner polyhedron by Gomory. Balas showed that intersection cuts are valid for the corner polyhedron. In this paper we show that, conversely, every nontrivial facet-defining inequality for the corner polyhedron is an intersection cut.

متن کامل

Lattice-free sets, multi-branch split disjunctions, and mixed-integer programming

In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and the multi-branch split cuts introduced by Li and Richard (2008). By analyzing n-dimensional lattice-free sets, we prove that for every integer n there exists a positive integer t such that every facet-defining inequality of the convex hull of a mixe...

متن کامل

The master equality polyhedron with multiple rows

The master equality polyhedron (MEP) is a canonical set that generalizes the Master Cyclic Group Polyhedron (MCGP) of Gomory. We recently characterized a nontrivial polar for the MEP, i.e., a polyhedron T such that an inequality defines a nontrivial facet of the MEP if and only if its coefficient vector forms a vertex of T . In this paper we study the MEP when it is defined by m > 1 rows. We de...

متن کامل

On the cardinality constrained matroid polytope

Given a combinatorial optimization problem Π and an increasing finite sequence c of natural numbers, we obtain a cardinality constrained version Πc of Π by permitting only those feasible solutions of Π whose cardinalities are members of c. We are interested in polyhedra associated with those problems, in particular in inequalities that cut off solutions of forbidden cardinality. Maurras [11] an...

متن کامل

Lattice-free sets, branching disjunctions, and mixed-integer programming

In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and structured disjunctive cuts, especially the t-branch split cuts introduced by Li and Richard (2008). By analyzing n-dimensional lattice-free sets, we prove that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set wit...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015