Definition
Let be a real normed vector space, and let be the dual space to . Denote the dual pairing by
For a functional
taking values on the extended real number line, the convex conjugate
is defined in terms of the supremum by
or, equivalently, in terms of the infimum by
This definition can be interpreted as an encoding of the convex hull of the function's epigraph in terms of its supporting hyperplanes.
Read more about this topic: Convex Conjugate
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