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IOR

2011

2011

In this paper, we give a ﬁnite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a ﬁnitely convergent convex hull tree algorithm which constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard notion of sequential cutting planes with ideas underlying the convex hull tree algorithm to help guide the choice of disjunctions to use within a cutting plane method. This algorithm, which we refer to as the cutting plane tree algorithm, is shown to converge to an integral optimal solution in ﬁnitely many iterations. Finally, we illustrate the proposed algorithm on three well-known examples in the literature that require an inﬁnite number of elementary or split disjunctions in a rudimentary cutting plane algorithm. Key words: Mixed-integer programming, disjunctive programming, convex hull, ﬁnite convergence.

Related Content

Added |
14 May 2011 |

Updated |
14 May 2011 |

Type |
Journal |

Year |
2011 |

Where |
IOR |

Authors |
Binyuan Chen, Simge Küçükyavuz, Suvrajeet Sen |

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