Extreme point

Summary

An extreme point of a convex set is a point of the set that lies strictly inside no segment between two other points of it. Extreme points are the corners of a convex set. The Krein–Milman theorem says that a compact convex set in a locally convex space is rebuilt from its extreme points by taking closed convex hulls. They also matter in linear optimization, where a linear function on a compact convex set in $\R^n$ reaches its maximum at an extreme point.