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In this paper, we develop a splitting algorithm incorporating Bregmandistances to solve a broad class of linearly constrained composite optimizationproblems, whose objective function is the separable sum of possibly nonconvexnonsmooth functions and a smooth function, coupled by a difference offunctions. This structure encapsulates numerous significant nonconvex andnonsmooth optimization problems in the current literature including thelinearly constrained difference-of-convex problems. Relying on the successivelinearization and alternating direction method of multipliers (ADMM), theproposed algorithm exhibits the global subsequential convergence to astationary point of the underlying problem. We also establish the convergenceof the full sequence generated by our algorithm under the Kurdyka-Lojasiewiczproperty and some mild assumptions. The efficiency of the proposed algorithm istested on a robust principal component analysis problem and a nonconvex optimalpower flow problem.

Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions