Convex function

In mathematics, a convex function is any function with value of the weighted average of 2 points is less than or equal to the weighted average of the function at those points. Also, a function is convex if and only if its epigraph is a convex set.

Convex function on an interval.

A function (in black) is convex if and only if the region above its graph (in green) is a convex set.

Examples

Three examples are:

• A line: $f(x)=x$
• A parabola: $f(x)=x^{2}$
• Absolute value: $f(x)=|x|$