Lift-and-Project Cuts: Properties of the Cut LP

This paper documents my research at GSIA, Carnegie Mellon University, during the summer of 1998. Topics on various aspects of the lift-and-project procedure are presented here. The overall theme binding all the results together here is the cut LP itself. One of the more promising results is an observation that the optimal solution to the cut LP will always contain a partition of all constraints. This hints at a possible reduction of the cut LP by performing an a priori partition of the constraints with the aim of simplifying the cut LP. Results are presented which suggests that such a partition might indeed be feasible. Other aspects of the cut LP presented here concerns the normalization constraint. I explore some polyhedral properties of different choices of normalization constraints. The mixed-integer Gomory cut is derived from a disjunction on the congruens based on one row of the simplex tableau. I show in this paper that a disjunction based on such a congruens is equivalent to a basic disjunction (xi 0)_ (xi 1) in the presence of cut strengthening.