Partial symmetric regularized alternating direction method of multipliers for non-convex split feasibility problems

In this paper, we propose a kind of partial symmetric regularized alternating direction method of multipliers for solving non-convex split feasibility problems. This algorithm adds an update to the Lagrangian multiplier term during the iteration process. Existing results about ADMM cannot be widely applied because the problem under consideration does not satisfy the assumptions usually claimed. The global convergence of the algorithm is proved under appropriate assumptions. And when the augmented Lagrangian function satisfies the KL property, the strong convergence of the algorithm is obtained. Furthermore, when the correlation function has a special structure, the sublinear and linear convergence rates of the algorithm are ensured. Finally, numerical experiments are conducted to show that the algorithm is effective.