Integer and combinatorial optimization
Integer and combinatorial optimization
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
On the Matrix-Cut Rank of Polyhedra
Mathematics of Operations Research
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Combinatorica
Two row mixed-integer cuts via lifting
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
On the rank of cutting-plane proof systems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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A cutting-plane procedure for integer programming (IP) problems usually involves invoking a black-box procedure (such as the Gomory-Chvátal (GC) procedure) to compute a cutting-plane. In this paper, we describe an alternative paradigm of using the same cuttingplane black-box. This involves two steps. In the first step, we design an inequality cx ≤ d, independent of the cutting-plane black-box. In the second step, we verify that the designed inequality is a valid inequality by verifying that the set P ∩ {x ε Rn : cx ≥ d + 1} ∩ Zn is empty using cutting-planes from the black-box. Here P is the feasible region of the linear-programming relaxation of the IP. We refer to the closure of all cutting-planes that can be verified to be valid using a specific cuttingplane black-box as the verification closure of the considered cutting-plane black-box. This paper conducts a systematic study of properties of verification closures of various cutting-plane black-box procedures.