Convex Hull

Created: 19.02.2022 | Updated: 19.02.2022

The convex hull of the set $C$ is the set of all the [Convex Combination] of the points in $C$ . It is denoted as $c o n v C$ and is always a [Convex Set] . The convex hull of a set is the smallest convex set containing that set. If $B$ is a convex set containing $C$ , then $c o n v C \subseteq B$ .

c o n v C = {θ_{1} x_{1} + \dots θ_{k} x_{k} ∣ x_{i} \in C, θ_{i} \geq 0, i = 1, \dots, k, θ_{1} + \dots + θ_{k} = 1}