k-Disjunctive cuts and a finite cutting plane algorithm for general mixed integer linear programs

In this paper we give a generalization of the well known split cuts of Cook, Kannan and Schrijver to cuts which are based on multi-term disjunctions. They will be called k-disjunctive cuts. The starting point is the question what kind of cuts is needed for a finite cutting plane algorithm for general mixed integer programs. We will deal with this question in detail and derive cutting planes based on k-disjunctions related to a given cut vector. Finally we will show how a finite cutting plane algorithm can be established using these cuts in combination with Gomory mixed integer cuts.