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Notions of Maximality for Integral Lattice-Free Polyhedra: The Case of Dimension Three

Notions of Maximality for Integral Lattice-Free Polyhedra: The Case of Dimension Three

Lattice-free sets and their applications for cutting-plane methods in mixed-integer optimization have been studied in recent literature. The family of all integral lattice-free polyhedra that are not properly contained in another integral lattice-free polyhedron has been of particular interest. We call these polyhedra ℤ d -maximal. For fixed d, the …