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Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

Binyuan Chen (bychen***at***email.arizona.edu)
Simge Kucukyavuz (kucukyavuz.2***at***osu.edu)
Suvrajeet Sen (sen.22***at***osu.edu)

Abstract: 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.

Keywords: Mixed-integer programming, disjunctive programming, convex hull, finite convergence

Category 1: Integer Programming (Cutting Plane Approaches )

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Citation: Technical report, Data Driven Decisions Lab, The Ohio State University

Download: [PDF]

Entry Submitted: 08/25/2009
Entry Accepted: 08/26/2009
Entry Last Modified: 03/07/2010

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