Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:Game_theory
gptkb:Control_theory Economics Machine learning Optimization |
| gptkbp:definedIn |
A set in 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:Polygon
gptkb:Affine_subspace gptkb:Annulus gptkb:Euclidean_ball gptkb:Star-shaped_set |
| gptkbp:field |
gptkb:Mathematics
gptkb:Convex_geometry Functional analysis |
| gptkbp:hasProperty |
Convex sets are path-connected
Convex sets are simply connected The convex hull of a set is convex Closed convex sets are important in functional analysis Every convex set in a finite-dimensional space is the intersection of half-spaces |
| https://www.w3.org/2000/01/rdf-schema#label |
Convex sets
|
| gptkbp:property |
Closed under convex combinations
Intersection of convex sets is convex Convex hull of any set is the smallest convex set containing it |
| gptkbp:relatedConcept |
gptkb:Convex_function
gptkb:Supporting_hyperplane Convex hull Extreme point |
| gptkbp:studiedBy |
gptkb:Hermann_Minkowski
gptkb:John_von_Neumann gptkb:Carathéodory |
| gptkbp:bfsParent |
gptkb:Minkowski's_theorem
|
| gptkbp:bfsLayer |
6
|