Abstract
We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory–Johnson model. These notions were known to coincide for continuous piecewise linear functions with rational breakpoints. We show that two of the notions, extreme functions and facets, coincide for the case of continuous piecewise linear functions, removing the hypothesis regarding rational breakpoints. We then separate the three notions using discontinuous examples.
The authors gratefully acknowledge partial support from the National Science Foundation through grant DMS-1320051, awarded to M. Köppe.
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Köppe, M., Zhou, Y. (2017). On the Notions of Facets, Weak Facets, and Extreme Functions of the Gomory–Johnson Infinite Group Problem. In: Eisenbrand, F., Koenemann, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2017. Lecture Notes in Computer Science(), vol 10328. Springer, Cham. https://doi.org/10.1007/978-3-319-59250-3_27
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DOI: https://doi.org/10.1007/978-3-319-59250-3_27
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