The regularized CQ algorithm without a priori knowledge of operator norm for solving the split feasibility problem

Abstract

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The split feasibility problem (SFP) is finding a point ...... such that ......, where C and Q are nonempty closed convex subsets of Hilbert spaces ...... and ......, and ...... is a bounded linear operator. Byrne's CQ algorithm is an effective algorithm to solve the SFP, but it needs to compute ......, and sometimes ...... is difficult to work out. López introduced a choice of stepsize ......, ......, ....... However, he only obtained weak convergence theorems. In order to overcome the drawbacks, in this paper, we first provide a regularized CQ algorithm without computing ...... to find the minimum-norm solution of the SFP and then obtain a strong convergence theorem.