Convex Set
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A Convex Set is an Euclidean space object where the straight line between any point pair is also completely within the object.
- Context:
- It can be bounded by a Convex Curve.
- See: Convex Function, Cube (Geometry), Crescent, Optimization Algorithm, Convex Surface.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Convex_set Retrieved:2014-9-28.
- In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins the pair of points is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex. A convex curve forms the boundary of a convex set.
The notion of a convex set can be generalized to other spaces as described below.
- In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins the pair of points is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex. A convex curve forms the boundary of a convex set.
1997
- (Luenberger, 1997) ⇒ David G. Luenberger. (1997). “Optimization by Vector Space Methods." Wiley Professional. ISBN:047118117X