# Cutting plane

### From Glossary

A hyperplane whose halfspace cuts off a particular point, such as a non-integer extreme point solution of a linear program relaxation of an integer program. The cut is such that it does not eliminate any solution to the original problem. For example, suppose we want to solve

The only feasible point is . The LP relaxation is

and an optimal solution is at . One cutting plane is
. A *deeper* one is .
(When adding a cutting plane to the LP, a new relaxation is obtained, and the solution is closer to the IP solution.)