Distributed Big-Data Optimization via Blockwise Gradient Tracking

We study distributed big-data nonconvex optimization in multiagent networks. consider the (constrained) minimization of sum a smooth (possibly) function, i.e., agents' sum-utility, plus convex nonsmooth regularizer. Our interest is on problems which there large number variables to optimize. If treated by means standard algorithms, these large-scale may be intractable due prohibitive local computation and communication burden at each node. propose novel solution method where, iteration, agents update an uncoordinated fashion only one block entire decision vector. To deal with nonconvexity cost scheme hinges successive approximation techniques combined blockwise perturbed push-sum consensus protocol, instrumental perform block-averaging operations tracking gradient averages. Asymptotic convergence stationary solutions problem established. Finally, numerical results show effectiveness proposed algorithm highlight how dimension impacts overhead practical speed.