= Exposed point
{wiki}
An <exposed point> is a <point> uniquely selected by maximizing a <linear functional>. In $\mathbb R^d$, a <point> $p$ of a <convex set> $C$ is exposed if some <vector> $c$ satisfies
$$
c^{\mathsf T}p>c^{\mathsf T}z\qquad(z\in C,\ z\ne p).
$$
Geometrically, a <supporting hyperplane> touches the <convex set> only at $p$. Every <exposed point> is an <extreme point>: a <convex combination> that attains the maximum can put positive weight only on maximizers, and there is only one.<Convex geometry (BME course BMETE94AM22)>[§6, Definition 6.2 and Proposition 6.7, printed pp. 36–37: exposed points and their inclusion among extremal points]{ref}
The <unit disk> calculation in <extreme point> exposes every <point> of the <unit circle>. For a corner $(a,b)$ of the <square>, $c=(a,b)$ exposes it: $ax+by$ attains two only at $(a,b)$. However, maximizing $x$ exposes no single <point> on the right edge, since all of them have the same objective value. A <linear functional> may have several optimal <points>, even when some of them are extreme.
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