Convex function

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File:ConvexFunction.svg
Convex function on an interval.
File:Epigraph convex.svg
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]

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