lower convex envelope

In mathematics, the lower convex envelope $\backslash breve\; f$ 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] \}.