Functional.convex_conj¶

property Functional.convex_conj¶

Convex conjugate functional of the functional.

Notes

The convex conjugate functional of a convex functional $f(x)$ , defined on a Hilber space, is defined as the functional

$f^*(x^*) = \sup_{x} \{ \langle x^*,x \rangle - f(x) \}.$

The concept is also known as the Legendre transformation.

For literature references see, e.g., [Lue1969], [Roc1970], the wikipedia article on Convex conjugate or the wikipedia article on the Legendre transformation.

References

[Lue1969] Luenberger, D G. Optimization by vector space methods. Wiley, 1969.

[Roc1970] Rockafellar, R. T. Convex analysis. Princeton University Press, 1970.