  In the applications of signal processing and data analytics, there is a wide
class of non-convex problems whose objective function is freed from the common
global Lipschitz continuous gradient assumption (e.g., the nonnegative matrix
factorization (NMF) problem). Recently, this type of problem with some certain
special structures has been solved by Bregman proximal gradient (BPG). This
inspires us to propose a new Block-wise two-references Bregman proximal
gradient (B2B) method, which adopts two reference functions so that a
closed-form solution in the Bregman projection is obtained. Based on the
relative smoothness, we prove the global convergence of the proposed algorithms
for various block selection rules. In particular, we establish the global
convergence rate of $O(\frac{\sqrt{s}}{\sqrt{k}})$ for the greedy and
randomized block updating rule for B2B, which is $O(\sqrt{s})$ times faster
than the cyclic variant, i.e., $O(\frac{s}{\sqrt{k}} )$, where $s$ is the
number of blocks, and $k$ is the number of iterations. Multiple numerical
results are provided to illustrate the superiority of the proposed B2B compared
to the state-of-the-art works in solving NMF problems.
