Convex function
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A function (in black) is convex if and only if the region above its graph (in green) is a convex set.
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.
Examples
Three examples are:
- A line: [math]\displaystyle{ f(x) = x }[/math]
- A parabola: [math]\displaystyle{ f(x) = x^2 }[/math]
- Absolute value: [math]\displaystyle{ f(x) = |x| }[/math]
Convex Function Media
A graph of the bivariate convex function x2 + xy + y2.