Convex Function - Definition

Definition

A real valued function f : XR defined on a convex set X in a vector space is called convex if, for any two points and in X and any ,

The function is called strictly convex if

for every, and .

A function f is said to be (strictly) concave if −f is (strictly) convex.

Read more about this topic:  Convex Function

Famous quotes containing the word definition:

    According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.
    Ana Castillo (b. 1953)

    The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.
    Samuel Taylor Coleridge (1772–1834)

    ... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.
    George Eliot [Mary Ann (or Marian)