Approximating Curve and Strong Convergence of the <it>CQ</it> Algorithm for the Split Feasibility Problem

Abstract

<p/> <p>Using the idea of Tikhonov's regularization, we present properties of the approximating curve for the split feasibility problem (SFP) and obtain the minimum-norm solution of SFP as the strong limit of the approximating curve. It is known that in the infinite-dimensional setting, Byrne's <it>CQ</it> algorithm (Byrne, 2002) has only weak convergence. We introduce a modification of Byrne's <it>CQ</it> algorithm in such a way that strong convergence is guaranteed and the limit is also the minimum-norm solution of SFP.</p