##  [Fenchel Conjugate](/fenchel-conjugate) 

  ##  [Fenchel Conjugate](https://natural.quantumdictionary.io/fenchel-conjugate-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For an extended-real-valued function f on a vector space, the Fenchel conjugate f* is the function f*(y) = sup_x (⟨y,x⟩ − f(x)), mapping primal cost functions to convex dual representations.