Support function

Summary

The support function of a nonempty set $A \subseteq \R^n$ assigns to each vector $x$ the supremum of the dot products $x \cdot a$ over $a \in A$. It is a sublinear function, and it determines a nonempty compact convex set completely. Support functions turn geometric operations into analytic ones: the support function of a Minkowski sum is the sum of the support functions. They are a basic tool in the study of convex bodies.