Let $V$ be a real [vector space](/page/Vector%20Space), let $C \subset V$ be convex, let $m \in \mathbb{N}$, let $f_i:C\to\mathbb{R}$ be convex for each $i \in \{1,\ldots,m\}$, and let $a_i \ge 0$ for each $i \in \{1,\ldots,m\}$. Define the function $f:C\to\mathbb{R}$ by