A Self-adaptive Super Set-relaxed Projection Method for Multiple-sets Split Feasibility Problem with Multiple Output Sets

This paper introduces an inertial accelerated super set-relaxed CQ method to solve a multiple-sets split feasibility problem with multiple output sets. The convex subsets involved are assumed to be level subsets of given strongly convex functions. Instead of using the involved sets, we approximate the original convex subsets with a sequence of closed balls. The proposed method is easy to implement as the projection onto the closed ball has a closed form. Additionally, we develop a new self-adaptive step-size that does not require any prior information of the norm. Under suitable assumptions, we establish and prove a strong convergence result for the algorithm. Numerical experiments are provided to demonstrate the performance of the proposed algorithm, which generalizes and improves upon existing literature.