Statements (37)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
optimization problems
sets functions |
| gptkbp:characterizedBy |
gptkb:Jensen's_inequality
supporting hyperplane theorem separation theorem |
| gptkbp:defines |
A set is convex if for any two points in the set, the line segment joining them is also in the set.
A function is convex if its epigraph is a convex set. |
| gptkbp:generalizes |
quasiconvexity
star-convexity strict convexity uniform convexity |
| gptkbp:hasProperty |
convex hull
convex combination convex functions have global minima convex sets are closed under convex combinations convex sets are path-connected intersection of convex sets is convex sum of convex functions is convex convex functions are continuous on the interior of their domain |
| https://www.w3.org/2000/01/rdf-schema#label |
convexity (mathematics)
|
| gptkbp:importantFor |
gptkb:machine_learning
gptkb:probability_theory functional analysis game theory linear programming |
| gptkbp:opposedBy |
concavity (mathematics)
|
| gptkbp:relatedTo |
convex set
convex function |
| gptkbp:studiedBy |
gptkb:mathematician
|
| gptkbp:usedIn |
gptkb:geometry
economics optimization convex analysis |
| gptkbp:bfsParent |
gptkb:Convex_geometry
|
| gptkbp:bfsLayer |
7
|