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

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

2007-07-26

arxiv.org/abs/0707.3945v1

Mathematics

Optimization and Control

18 pages, 2 figures

Scientific paper

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.

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