Weighted average and Epigraph (mathematics): Difference between pages
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A | [[Image:Epigraph convex.svg|right|thumb|300px|A function (in black) is [[convex function|convex]] if and only if the region above its [[graph]] (in green) is a [[convex set]].]] | ||
In [[mathematics]], the '''epigraph''' of a [[Function (mathematics)|function]] is the set of paired values so the output of the function at the first value is [[less than or equal to]] the second value. In math terms this means <math>(x,r) \in \operatorname{epi}(f)</math> [[if and only if]] <math>f(x) \leq r</math>. | |||
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[[Category:Mathematics]] | [[Category:Mathematics]] |
Latest revision as of 00:17, 17 April 2013
In mathematics, the epigraph of a function is the set of paired values so the output of the function at the first value is less than or equal to the second value. In math terms this means [math]\displaystyle{ (x,r) \in \operatorname{epi}(f) }[/math] if and only if [math]\displaystyle{ f(x) \leq r }[/math].