Content deleted Content added
m Open access bot: arxiv updated in citation with #oabot. |
only in 2d |
||
Line 6:
For example, a solid [[cube (geometry)|cube]] is a convex set, but anything that is hollow or has an indent, for example, a [[crescent]] shape, is not convex.
The [[boundary (topology)|boundary]] of a convex set in the plane is always a [[convex curve]]. The intersection of all the convex sets that contain a given subset {{mvar|A}} of Euclidean space is called the [[convex hull]] of {{mvar|A}}. It is the smallest convex set containing {{mvar|A}}.
A [[convex function]] is a [[real-valued function]] defined on an [[interval (mathematics)|interval]] with the property that its [[epigraph (mathematics)|epigraph]] (the set of points on or above the [[graph of a function|graph]] of the function) is a convex set. [[Convex minimization]] is a subfield of [[mathematical optimization|optimization]] that studies the problem of minimizing convex functions over convex sets. The branch of mathematics devoted to the study of properties of convex sets and convex functions is called [[convex analysis]].
| |||