Weak and strong convergence of a general splitting approach for monotone multioperator inclusions

In this paper, we study a general forward-backward splitting approach for monotone inclusion problems that simultaneously accommodate set-valued, monotone Lipschitz continuous, and cocoercive operators. Weak convergence is established under a general setting. Strong convergence is obtained when both the maximally monotone operators are linear relations and the monotone Lipschitz continuous and cocoercive operators are linear. When the set-valued operators are normal cones to closed linear subspaces, we derive an explicit characterization of limit points of generated sequences using a new technique. Numerical experiments on a quadratic minimization problem with multiple-set split feasibility constraints are presented to illustrate the theoretical results.