A SELF-ADAPTIVE INERTIAL VISCOSITY PROJECTION ALGORITHM FOR SOLVING SPLIT FEASIBILITY PROBLEM WITH MULTIPLE OUTPUT SETS

We propose an inertial viscosity projection algorithm for solving the split feasibility problem with multiple output sets in the Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive technique which does not require prior information about operator norm. In addition, the inertial technique and viscosity method are combined to improve the convergence. Under suitable conditions, we show the strong convergence of the algorithm. Furthermore, we present new results on the algorithm for solving the split feasibility problem and split feasibility problem with multiple output sets. Finally, two numerical experiments are presented to illustrate the convergence behavior and the effectiveness of the algorithm.