Convex function

real function with secant line between points above the graph itself

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 Edit

Three examples are:

  • A line:  
  • A parabola:  
  • Absolute value: