Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
convex analysis |
| gptkbp:alsoKnownAs |
convex conjugate
|
| gptkbp:application |
gptkb:machine_learning
gptkb:statistical_mechanics gptkb:Lagrangian_duality economics |
| gptkbp:defines |
The Fenchel conjugate of a function f is the function f* defined by f*(y) = sup_x (⟨y, x⟩ - f(x)).
|
| https://www.w3.org/2000/01/rdf-schema#label |
Fenchel conjugate
|
| gptkbp:namedAfter |
gptkb:Werner_Fenchel
|
| gptkbp:property |
The biconjugate of a function is the greatest lower semicontinuous convex function less than or equal to the original function.
The Fenchel conjugate of a lower semicontinuous convex function is lower semicontinuous. The Fenchel conjugate of a convex function is convex. |
| gptkbp:relatedTo |
duality
Legendre transform biconjugate subdifferential |
| gptkbp:usedIn |
mathematical analysis
optimization |
| gptkbp:bfsParent |
gptkb:Convex_Analysis
gptkb:Rockafellar's_duality_theory |
| gptkbp:bfsLayer |
6
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