Lower convex envelope

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

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

See also

• Convex hull
• Lower envelope