# Gomory cut

### From Glossary

This is an early cutting plane for an
integer program. Consider
,
where and have integer values. For any ,
let and
(i.e., is
the fractional part of the linear combination
of the equations, and is the fractional part of the same linear
combination of the right-hand sides). Also, let
(fractional part of ). Then, Gomory's cut is:

The vector is chosen such that and the current solution (with ) violates this inequality in the LP relaxation.