Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
gptkb:Convex_set
|
| gptkbp:defines |
A function f is convex if for any x, y in its domain and t in [0,1], f(tx + (1-t)y) ≤ t f(x) + (1-t) f(y).
|
| gptkbp:example |
gptkb:Exponential_function
gptkb:Quadratic_function Absolute value function |
| gptkbp:field |
gptkb:Mathematics
gptkb:Convex_analysis Optimization |
| gptkbp:generalizes |
Linear function
|
| https://www.w3.org/2000/01/rdf-schema#label |
Convex function
|
| gptkbp:opposedBy |
Concave function
|
| gptkbp:property |
Second derivative is non-negative (for twice differentiable functions)
Epigraph is a convex set Local minimum is global minimum |
| gptkbp:relatedConcept |
gptkb:Jensen's_inequality
gptkb:Convex_set Subgradient |
| gptkbp:usedIn |
Economics
Machine learning Convex optimization |
| gptkbp:bfsParent |
gptkb:Convex_sets
gptkb:Convex_set |
| gptkbp:bfsLayer |
7
|