split cuts

On mixed-integer sets with two integer variables

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

    We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined recently in another paper). We then extend this observation to show that crooked cross cuts give the convex hull of mixed-integer sets with more integer variables provided that … Read more

    A probabilistic comparison of split and type 1 triangle cuts for two row mixed-integer programs

  • Shabbir Ahmed
  • Qie He
  • George L. Nemhauser
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    We provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables. Under a simple probabilistic model of the problem parameters, we show that a simple split cut, i.e. a Gomory cut, is more likely to be better than a type 1 triangle cut in … Read more