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

X iv :0 70 7. 39 45 v1 [ m at h. O C ] 2 6 Ju l 2 00 7 k-disjun tive uts and a nite utting plane algorithm for general mixed integer linear programs Markus Jörg Te hnis he Universität Mün hen, Zentrum Mathematik Boltzmannstraÿe 3, 85747 Gar hing bei Mün hen, Germany joerg ma.tum.de July 26, 2007 Abstra t: In this paper we give a generalization of the well known split uts of Cook, Kannan and S hrijver [5℄ to uts whi h are based on multi-term disjun tions. They will be alled k-disjun tive uts. The starting point is the question what kind of uts is needed for a nite utting plane algorithm for general mixed integer programs. We will deal with this question in detail and derive utting planes based on k-disjun tions related to a given ut ve tor. Finally we will show how a nite utting plane algorithm an be established using these uts in ombination with Gomory mixed integer uts. 1 Introdu tion In this paper we will deal with utting planes and related algorithms for general mixed integer linear programs (MILP). As most of the results will be derived by geometri arguments we fo us on programs that are given by inequality onstraints, i.e.