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The alternating direction method with multipliers (ADMM) has been one of mostpowerful and successful methods for solving various convex or nonconvexcomposite problems that arise in the fields of image & signal processing andmachine learning. In convex settings, numerous convergence results have beenestablished for ADMM as well as its varieties. However, due to the absence ofconvexity, the convergence analysis of nonconvex ADMM is generally verydifficult. In this paper we study the Bregman modification of ADMM (BADMM),which includes the conventional ADMM as a special case and often leads to animprovement of the performance of the algorithm. Under certain assumptions, weprove that the iterative sequence generated by BADMM converges to a stationarypoint of the associated augmented Lagrangian function. The obtained resultsunderline the feasibility of ADMM in applications under nonconvex settings.

Convergence of Bregman alternating direction method with multipliers for nonconvex composite problems