FunctionalTranslation.convex_conj¶

property FunctionalTranslation.convex_conj¶

Convex conjugate functional of the translated functional.

Notes

Given a functional $f$ , the convex conjugate of a translated version $f(\cdot - y)$ is given by a linear pertubation of the convex conjugate of $f$ :

$(f( . - y))^* (x) = f^*(x) + <y, x>.$

For reference on the identity used, see [KP2015].

References

[KP2015] Komodakis, N, and Pesquet, J-C. Playing with Duality: An overview of recent primal-dual approaches for solving large-scale optimization problems. IEEE Signal Processing Magazine, 32.6 (2015), pp 31–54.