  In this paper, we develop a splitting algorithm incorporating Bregman
distances to solve a broad class of linearly constrained composite optimization
problems, whose objective function is the separable sum of possibly nonconvex
nonsmooth functions and a smooth function, coupled by a difference of
functions. This structure encapsulates numerous significant nonconvex and
nonsmooth optimization problems in the current literature including the
linearly constrained difference-of-convex problems. Relying on the successive
linearization and alternating direction method of multipliers (ADMM), the
proposed algorithm exhibits the global subsequential convergence to a
stationary point of the underlying problem. We also establish the convergence
of the full sequence generated by our algorithm under the Kurdyka-Lojasiewicz
property and some mild assumptions. The efficiency of the proposed algorithm is
tested on a robust principal component analysis problem and a nonconvex optimal
power flow problem.
