An exposed point is a point uniquely selected by maximizing a linear functional. In , a point of a convex set is exposed if some vector satisfiesGeometrically, a supporting hyperplane touches the convex set only at . 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.[ref]
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
The unit disk calculation in extreme point exposes every point of the unit circle. For a corner of the square, exposes it: attains two only at . However, maximizing 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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"Exposed Point" can refer to different concepts depending on the context, such as in mathematics, geography, or other fields. However, this term isn't universally defined as a standard term across disciplines. Here are some possible interpretations: 1. **Mathematics/Geometry**: In geometrical contexts, an exposed point can refer to a point on a polyhedron or surface that is not obscured by other parts of the shape.