Editing Convex conjugate (section)

{{Short description|Generalization of the Legendre transformation}}
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In [[mathematics]] and [[mathematical optimization]], the '''convex conjugate''' of a function is a generalization of the [[Legendre transformation]] which applies to non-convex functions. It is also known as '''Legendre–Fenchel transformation''', '''Fenchel transformation''', or '''Fenchel conjugate''' (after [[Adrien-Marie Legendre]] and [[Werner Fenchel]]).  The convex conjugate is widely used for constructing the [[Duality (optimization)|dual problem]] in [[optimization theory]], thus generalizing [[Duality (optimization)#Lagrange duality|Lagrangian duality]].