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:

    I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)