KullbackLeiblerConvexConj.bregman¶
- KullbackLeiblerConvexConj.bregman(point, subgrad)¶
Return the Bregman distance functional.
- Parameters:
- pointelement of
functional.domain
Point from which to define the Bregman distance.
- subgradelement of
functional.domain
A subgradient of
functional
inpoint
. If it exists, a valid option isfunctional.gradient(point)
.
- pointelement of
- Returns:
- out
BregmanDistance
The Bregman distance functional.
- out
Notes
Given a functional , a point , and a (sub)gradient , the Bregman distance functional in a point is given by
For mathematical details, see [Bur2016]. See also the Wikipedia article: https://en.wikipedia.org/wiki/Bregman_divergence
References
[Bur2016] Burger, M. Bregman Distances in Inverse Problems and Partial Differential Equation. In: Advances in Mathematical Modeling, Optimization and Optimal Control, 2016. p. 3-33.