# Extreme point

### From Glossary

A point in the closure of a set, say , that is not the midpoint of any open line segment with end points in closure of . Equivalently, is an extreme point of a closed set, , if there do not exist for which . When is a polyhedron of the standard form, , with of full row rank, we have one of the fundamental theorems of linear programming that underlies the simplex method:

is an extreme point of the feasible region if, and only if, is a basic feasible solution.