Lower convex envelope

In mathematics, the lower convex envelope ${\displaystyle {\breve {f}}}${\displaystyle {\breve {f}}} of a function ${\displaystyle f}${\displaystyle f} defined on an interval ${\displaystyle [a,b]}${\displaystyle [a,b]} is defined at each point of the interval as the supremum of all convex functions that lie under that function, i.e.

${\displaystyle {\breve {f}}(x)=\sup\{g(x)\mid g{\text{ is convex and }}g\leq f{\text{ over }}[a,b]\}.}${\displaystyle {\breve {f}}(x)=\sup\{g(x)\mid g{\text{ is convex and }}g\leq f{\text{ over }}[a,b]\}.}

• Convex hull
• Lower envelope

• Convex analysis
• Mathematical analysis stubs

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