Adaptively relaxed algorithms for solving the split feasibility problem with a new step size

Abstract

In the present paper, we propose several kinds of adaptively relaxed iterative algorithms with a new step size for solving the split feasibility problem in real Hilbert spaces. The proposed algorithms never terminate, while the known algorithms existing in the literature may terminate. Several weak and strong convergence theorems of the proposed algorithms have been established. Some numerical experiments are also included to illustrate the effectiveness of the proposed algorithms. MSC: Primary 46E20; 47J20; secondary 47J25

New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem

“…The experiments compare the performances of the proposed stepsizes of the CQ algorithm in this paper with the stepsizes in [15] and [16]. …”

A regularization algorithm for a splitting feasibility problem in Hilbert spaces

“…The split feasibility problem has recently been investigated via fixed point methods; see [9,11,13,18,20] and the references therein. Define a mapping A γ by…”

“…It is easy to see that Fix(A γ ) = A −1 (Q) and hence Sol(SFP) = C ∩ Fix(A γ ) = Fix(P C A γ ) for sufficiently small γ > 0; see Zhou and Wang [20] for the details. The rest of the paper is organized as follows.…”

The split feasibility problems in an infinite dimensional space

“…It is easy to see that Fix(U δ ) = A −1 (Q) and hence C U δ , respectively, for sufficiently small δ > 0; see Wang, Zhou [20], Zhou [21] and Zhou, Wang [22] for the details.…”