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.

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

See also

• Convex hull