In this paper, we study the relationship between 2D lattice-free cuts, the family of cuts obtained by taking two-row relaxations of a mixed-integer program (MIP) and applying intersection cuts based on maximal lattice-free sets in R, and various types of disjunctions. Recently, Li and Richard (2007) studied disjunctive cuts obtained from t-branch split disjunctions of mixed-integer sets (these ...

We consider the genus-one curves which arise in cuts of sunrise and elliptic double-box Feynman integrals. compute compare invariants these a number ways, including parametrization, lightcone Baikov (in full loop-by-loop variants). find that same geometry for arises all cases, lends support to idea there exists an invariant notion geometry, independent on way it is computed. further indicate ho...

We propose a new class of Foundation-Penalty (FP) cuts for GUB-constrained (and ordinary) mixed-integer programs, which are easy to generate by exploiting standard penalty calculations that are routinely employed in branch-and-bound contexts. The FP cuts are derived with reference to a selected integer variable or GUB set, and a foundation function that is typically a reduced cost function corr...