  We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing
the sum of a block relatively smooth function (that is, relatively smooth
concerning each block) and block separable nonsmooth nonconvex functions. We
prove that the sequence generated by BIBPA subsequentially converges to
critical points of the objective under standard assumptions, and globally
converges when the objective function is additionally assumed to satisfy the
Kurdyka-{\L}ojasiewicz (K{\L}) property. We also provide the convergence rate
when the objective satisfies the {\L}ojasiewicz inequality. We apply BIBPA to
the symmetric nonnegative matrix tri-factorization (SymTriNMF) problem, where
we propose kernel functions for SymTriNMF and provide closed-form solutions for
subproblems of BIBPA.
