An inertial extrapolation method for multiple-set split feasibility problem

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.

New hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem

“…In recent years, scholars have proposed some inertial iterative algorithms for solving the SFP. Based on [12], Taddele et al [21] proposed an iterative algorithm with inertial extrapolation to approximate the solution of multiple-set SFP. Shehu et al [18] introduced new CQ methods with alternated inertial procedure and selfadaptive stepsize for solving SFP.…”

Convergence Results on the General Inertial-Mann-Halpern and General Inertial Mann Algorithms

“…But the convergence rate of the Mann algorithm is slow in general. Due to the fact that fast convergence is required in many practical applications (see, [8,16,17,27]), many researchers constructed fast iterative algorithms by using inertial extrapolation methods (see [1,5,7,9,20,[32][33][34]). Specifically, Mainge [22] developed the following algorithm by employing the Mann algorithm together with inertial extrapolation method:…”