cross cuts

On the polyhedrality of cross and quadrilateral closures

  • Sanjeeb Dash
  • Oktay Gunluk
  • Diego Moran Ramirez
    • Categories (Mixed) Integer Linear Programming Tags , ,

    Split cuts form a well-known class of valid inequalities for mixed-integer programming problems. Cook, Kannan and Schrijver (1990) showed that the split closure of a rational polyhedron $P$ is again a polyhedron. In this paper, we extend this result from a single rational polyhedron to the union of a finite number of rational polyhedra. We … Read more

    Two dimensional lattice-free cuts and asymmetric disjunctions for mixed-integer polyhedra

  • Sanjeeb Dash
  • Santanu S. Dey
  • Oktay Gunluk
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    In this paper, we study the relationship between {\em 2D lattice-free cuts}, the family of cuts obtained by taking two-row relaxations of a mixed-integer program (MIP) and applying intersection cuts based on maximal lattice-free sets in $\R^2$, and various types of disjunctions. Recently, Li and Richard (2007) studied disjunctive cuts obtained from $t$-branch split disjunctions … Read more