# Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets

@article{Basu2011AlgorithmicAC, title={Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets}, author={Amitabh Basu and Robert Hildebrand and Matthias K{\"o}ppe}, journal={ArXiv}, year={2011}, volume={abs/1107.5068} }

We study a mixed integer linear program with m integer variables and k nonnegative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities from two rows of a simplex tableau, Proc. IPCO 2007, LNCS, vol. 4513, Springer, pp. 1{15]. We describe the facets of this mixed integer linear program via the extreme points of a well-dened polyhedron. We then utilize this description to give polynomial time…

## 8 Citations

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It is shown that when the number of integer variables $$m=2$$ the triangle closure is indeed a polyhedron and its number of facets can be bounded by a polynomial in the size of the input data.

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An introduction to a recently established link between the geometry of numbers and mixed integer optimization and a review of families of lattice-free polyhedra and their use in a disjunctive programming approach is given.

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A small subset of multi-row intersection cuts based on the infinity norm, which works for relaxations with arbitrary numbers of rows, and is concluded that these cuts yield benefits comparable to using the entire class ofmulti-row cuts, but at a small fraction of the computational cost.

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### Relaxations of mixed integer sets from lattice-free polyhedra

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An introduction to a recently established link between the geometry of numbers and mixed integer optimization and a review of families of lattice-free polyhedra and their use in a disjunctive programming approach is given.

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