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.

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

See also

• Convex hull
• Lower envelope