Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:Game_theory
gptkb:Control_theory Economics Machine learning Linear programming Operations research Optimization |
| gptkbp:closure_property |
Intersection of convex sets is convex
Arbitrary intersection of convex sets is convex Union of convex sets is not necessarily convex |
| gptkbp:definedIn |
A subset of a vector space such that for any two points in the set, the line segment joining them is also in the set
|
| gptkbp:example |
gptkb:Convex_polytope
gptkb:Annulus gptkb:Euclidean_ball gptkb:Star-shaped_set gptkb:Half-space Line segment Convex polygon |
| gptkbp:field |
gptkb:Mathematics
gptkb:Convex_geometry Functional analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Convex set
|
| gptkbp:mathematical_structure |
Subset of affine space
Subset of real vector space |
| gptkbp:property |
Closed under convex combinations
The convex hull of a set is convex Convex hull of a set is the smallest convex set containing it Convex sets are closed under affine transformations A convex set is unbounded if it contains a ray A convex set may be open, closed, or neither Convex sets are closed under intersection A convex set is a polyhedron if it is the intersection of finitely many half-spaces Every convex set is connected Every convex set is path-connected A convex set is a convex cone if it is closed under positive scalar multiplication A convex set is a simplex if it is the convex hull of affinely independent points A convex set in R^n is a convex body if it is compact and has non-empty interior Every convex set is simply connected (in Euclidean space) A convex set is bounded if and only if it is contained in a ball of finite radius The intersection of any family of convex sets is convex |
| gptkbp:relatedConcept |
gptkb:Convex_function
gptkb:Supporting_hyperplane gptkb:Affine_set gptkb:Convex_cone Convex hull Extreme point |
| gptkbp:subset_of |
gptkb:Vector
|
| gptkbp:bfsParent |
gptkb:Convex_polytope
|
| gptkbp:bfsLayer |
6
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