An inertial stochastic Bregman generalized alternating direction method of multipliers for nonconvex and nonsmooth optimization

The alternating direction method of multipliers (ADMM) is a widely employed first-order method due to its efficiency and simplicity. Nonetheless, like other splitting methods, ADMM’s performance degrades substantially as the scale of the optimization problems it addresses increases. This work is devoted to studying an accelerated stochastic generalized ADMM framework with a class of variance-reduced gradient estimators for solving large-scale nonconvex nonsmooth optimization problems with linear constraints, in which we combine inertial technique and Bregman distance. Under the assumption that the objective functions are semi-algebraic which satisfies the Kurdyka–Łojasiewicz (KL) property, we establish the global convergence and convergence rate of the sequence generated by our proposed algorithm. Finally, numerical experiments on conducting a graph-guided fused lasso illustrates the efficiency of the proposed method.