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In this paper, for solving a broad class of large-scale nonconvex andnonsmooth optimization problems, we propose a stochastic two step inertialBregman proximal alternating linearized minimization (STiBPALM) algorithm withvariance-reduced stochastic gradient estimators. And we show that SAGA andSARAH are variance-reduced gradient estimators. Under expectation conditionswith the Kurdyka-Lojasiewicz property and some suitable conditions on theparameters, we obtain that the sequence generated by the proposed algorithmconverges to a critical point. And the general convergence rate is alsoprovided. Numerical experiments on sparse nonnegative matrix factorization andblind image-deblurring are presented to demonstrate the performance of theproposed algorithm.

A stochastic two-step inertial Bregman proximal alternating linearized minimization algorithm for nonconvex and nonsmooth problems