CONJUGATE FUNCTION
Conjugate function - The convex conjugate of f on X, denoted f* on X*, is the greatest convex approximation from below:
f*(x*) = Sup( x*x' - f(x): x in X),
and X* = (x*: f*(x*) < infinity) (= effective domain of f*). The
concave conjugate of f on X, denoted f^ on X^, is the least concave approximation from above:
f^(x*) = Inf( x*x' - f(x): x in X),
and X^ = (x*: f^(x*) > -infinity). This is a foundation for Lagrangian duality , viewed in response space .
