Editing Extreme point (section)

{{short description|Point not between two other points}}
{{Other uses}}

[[Image:Extreme points.svg|thumb|right|A convex set in light blue, and its extreme points in red.]]

In [[mathematics]], an '''extreme point''' of a [[convex set]] <math>S</math> in a [[Real number|real]] or [[Complex number|complex]] [[vector space]] is a point in <math>S</math> that does not lie in any open [[line segment]] joining two points of <math>S.</math> The extreme points of a line segment are called its ''[[endpoint (geometry)|endpoints]]''. In [[linear programming]] problems, an extreme point is also called ''[[vertex (geometry)|vertex]]'' or ''corner point'' of <math>S.</math><ref>{{Cite web|url=https://www.quora.com/What-is-the-difference-between-corner-points-and-extreme-points-in-linear-programming-problems|title=What is the difference between corner points and extreme points in linear programming problems?|last=Saltzman|first=Matthew}}</ref>