Convex function

real function with secant line between points above the graph itself From Wikipedia, the free encyclopedia

Convex function
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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.

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Convex function on an interval.
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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.

Examples

Three examples are:

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