18 citations · 51 across the 11 of their papers we have counts for
5 papers · 1 filter
On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem
Matthias Köppe, Yuan Zhou
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 kn…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. V. Software for the continuous and discontinuous 1-row case
Chun Yu Hong, Matthias Köppe, Yuan Zhou
We present software for investigations with cut-generating functions in the Gomory--Johnson model and extensions, implemented in the computer algebra system SageMath.
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The curious case of two-sided discontinuous minimal valid functions
Matthias Köppe, Yuan Zhou
We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory--Johnson model which is not extreme, but which is not a convex combination of ot…
Software for cut-generating functions in the Gomory--Johnson model and beyond
Chun Yu Hong, Matthias Köppe, Yuan Zhou
We present software for investigations with cut generating functions in the Gomory-Johnson model and extensions, implemented in the computer algebra system SageMath.
Toward computer-assisted discovery and automated proofs of cutting plane theorems
Matthias Köppe, Yuan Zhou
Using a metaprogramming technique and semialgebraic computations, we provide computer-based proofs for old and new cutting-plane theorems in Gomory--Johnson's model of cut generati…