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m The first sentence was incorrect, if the line segment had to be above the graph then f(x) = cx is not convex. I believe the previous author was in a hurry, this is a minor edit. Please search for ORF523_S16_Lec7_gh.pdf to see an introduction to the topic if this change feels strange. |
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[[File:Convex vs. Not-convex.jpg|thumb|right|300px|Convex vs. Not convex]]
In [[mathematics]], a [[real-valued function]] is called '''convex''' if the [[line segment]] between any two distinct points on the [[graph of a function|graph of the function]] lies above or on the graph between the two points. Equivalently, a function is convex if its [[epigraph (mathematics)|''epigraph'']] (the set of points on or above the graph of the function) is a [[convex set]].
In simple terms, a convex function graph is shaped like a cup <math>\cup</math> (or a straight line like a linear function), while a [[concave function]]'s graph is shaped like a cap <math>\cap</math>.
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