Lower convex envelope

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



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