# Literature on convergence of Bregman divergences

#### gumbel

##### New Member
Hi,

as the title indicates, I am looking for some literature related to convergence properties of Bregman divergences. Generally speaking, I am interested whether and under which conditions Bregman divergences between a sequence of functions and another function converge as the sequence of functions converges.

I was hoping someone around here could point me to some relevant papers as starting points for further literature research.

#### BGM

##### TS Contributor
First time to heard this term. Just my two cents.

I have read that the Bregman divergence $$d_F(p,q) = 0 \iff p = q$$

Suppose $$\|p - q\| \to 0$$ under certain norm $$\|\cdot\|$$

I think one of the most obvious conditions is that $$d_F$$ is a continuous functional which should be able to guarantee the convergence. Of course there are different type of continuity and one maybe able to relax the condition.

Hopefully there are other experts to give more insight on this.

#### gumbel

##### New Member
I think one of the most obvious conditions is that $$d_F$$ is a continuous functional which should be able to guarantee the convergence. Of course there are different type of continuity and one maybe able to relax the condition.

.
Thank your for the first reply, this is exactly what I am searching literature results for.