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

The split feasibility problem (SFP) is finding a point [Formula: see text] such that [Formula: see text] , where C and Q are nonempty closed convex subsets of Hilbert spaces [Formula: see text] and [Formula: see text] , and [Formula: see text] is a bounded linear operator. Byrne’s CQ algorithm is an effective algorithm to solve the SFP, but it needs to compute [Formula: see text] , and sometimes [Formula: see text] is difficult to work out. López introduced a choice of stepsize [Formula: see text] , [Formula: see text] , [Formula: see text] . 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 [Formula: see text] to find the minimum-norm solution of the SFP and then obtain a strong convergence theorem.