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How to find the convex hull of all integer points in a polyhedron?

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Abstract

We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our algorithm, DDMCuts, is based on the Gomory cuts and the dynamic version of the double description method. We describe the computer implementation of the algorithm and present the results of computational experiments comparing our algorithm with a naive one and an algorithm implemented in Normaliz.

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Acknowledgements

This work was supported by the Scientific and Education Mathematical Center “Mathematics for Future Technologies” (Project No. 075-02-2020-1483/1). The authors are grateful to prof. Winfried Bruns for helpful discussions.

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Correspondence to N. Yu. Zolotykh.

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Semenov, S.O., Zolotykh, N.Y. How to find the convex hull of all integer points in a polyhedron?. Optim Lett 16, 2177–2189 (2022). https://doi.org/10.1007/s11590-021-01729-w

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  • DOI: https://doi.org/10.1007/s11590-021-01729-w

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