  In this paper, we consider a class of nonsmooth nonconvex optimization
problems whose objective is the sum of a block relative smooth function and a
proper and lower semicontinuous block separable function. Although the analysis
of block proximal gradient (BPG) methods for the class of block $L$-smooth
functions have been successfully extended to Bregman BPG methods that deal with
the class of block relative smooth functions, accelerated Bregman BPG methods
are scarce and challenging to design. Taking our inspiration from Nesterov-type
acceleration and the majorization-minimization scheme, we propose a block
alternating Bregman Majorization-Minimization framework with Extrapolation
(BMME). We prove subsequential convergence of BMME to a first-order stationary
point under mild assumptions, and study its global convergence under stronger
conditions. We illustrate the effectiveness of BMME on the penalized orthogonal
nonnegative matrix factorization problem.
