Extreme Point

Extreme Point
In mathematics, an extreme point of a convex set S in a Real number, real or Complex number, complex vector space is a point in S that does not lie in any open line segment joining two points of S. 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 S. Definition Throughout, it is assumed that X is a Real number, real or Complex number, complex vector space. For any p, x, y \in X, say that p x and y if x \neq y and there exists a 0 < t < 1 such that

p = t x + (1-t) y.

K

is a subset of

X

and

p \in K,

then

p

is called an of

K

if it does not lie between any two points of

K.

That is, if there does exist

x, y \in K

and

0 < t < 1

such that

x \neq y

and

p = t x + (1-t) y.

The s ...
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Extreme Points
In mathematics, an extreme point of a convex set S in a real or complex vector space is a point in S that does not lie in any open line segment joining two points of S. The extreme points of a line segment are called its '' endpoints''. In linear programming problems, an extreme point is also called '' vertex'' or ''corner point'' of S. Definition Throughout, it is assumed that X is a real or complex vector space. For any p, x, y \in X, say that p x and y if x \neq y and there exists a 0 < t < 1 such that

p = t x + (1-t) y.

K

is a subset of

X

and

p \in K,

then

p

is called an of

K

if it does not lie between any two points of

K.

That is, if there does exist

x, y \in K

and

0 < t < 1

such that

x \neq y

and

p = t x + (1-t) y.

The set of all extreme points of

K

is denoted by

\operatorname(K).

Gener ...
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