An inertial extrapolation method for multiple-set split feasibility problem

Abstract

Abstract In this paper, we propose an iterative algorithm with inertial extrapolation to approximate the solution of multiple-set split feasibility problem. Based on Lopez et al. (Inverse Probl. 28(8):085004, 2012), we have developed a self-adaptive technique to choose the stepsizes such that the implementation of our algorithm does not need any prior information about the operator norm. We then prove the strong convergence of a sequence generated by our algorithm. We also present numerical examples to illustrate that the acceleration of our algorithm is effective.

Keywords

• Multiple-set split feasibility problem
• Sublevel set
• Subdifferential
• Inertial extrapolation
• Self-adaptive technique