Inertial CQ Algorithm With Correction Terms for Split Feasibility Problems With Multiple Output Sets

Abstract

We propose a new CQ algorithm which combines the inertial technique and correction terms for solving the split feasibility problem with multiple output sets in Hilbert spaces. Under suitable conditions, we prove the weak convergence. Moreover, we demonstrate the linear convergence when the split feasibility problem with multiple output sets satisfies some bounded linear regularity property. Finally, numerical experiments are conducted to demonstrate superiority of our method over related inertial CQ method and classical CQ method for the split feasibility problem with multiple output sets.