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

This paper documents my research at GSIA, Carnegie Mellon University, during the sum- mer of 1998. Topics on various aspects of the lift-and-proje ct procedure are presented here. The overall theme binding all the results together here is th e 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 hin ts 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 normali zation 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.