The convex hull of the set \(C\) is the set of all the [Convex Combination] of the points in \(C\). It is denoted as \(conv C\) 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 \(conv C \subseteq B\).
\[conv C = \{ \theta_1 x_1 + \dots \theta_k x_k \mid x_i \in C, \theta_i \geq 0, i = 1, \dots, k, \theta_1 + \dots + \theta_k =1 \}\]