Abstract
In this paper, we study the alternating CQ algorithm for solving the split equality problem in Hilbert spaces. It is, however, not easy to implement since its selection of the stepsize requires prior information on the norms of bounded linear operators. To avoid this difficulty, we propose several modified algorithms in which the selection of the stepsize is independent of the norms. In particular, we consider the case whenever the convex sets involved are level sets of given convex functions.
Highlights
The split feasibility problem (SFP) requires finding a point x ∈ H1 satisfying the property x ∈ C and Ax ∈ Q, (1)where A : H1 → H2 is a bounded linear operator, and C and Q are two nonempty closed and convex subsets of Hilbert spaces H1 and H2, respectively
Motivated by the choice of stepsize (6), we propose three alternating iterative algorithms for the split equality problem (SEP), in which the choice of the stepsize is independent of the norms A and B
We aim to introduce the following alternating iterative algorithm which does not depend on the norms
Summary
The split feasibility problem (SFP) requires finding a point x ∈ H1 satisfying the property x ∈ C and Ax ∈ Q, (1)where A : H1 → H2 is a bounded linear operator, and C and Q are two nonempty closed and convex subsets of Hilbert spaces H1 and H2, respectively. Lemma 2.8 ([25]) Let {xn} be a sequence in H satisfying the properties: (i) limn→∞ xn – x exists for each x ∈ C; (ii) ωw(xn) ⊆ C. From Lemma 2.3 and the obvious fact that xn ∈ C, it follows that xn+1 – xn = PC xn – τnA∗(Axn – Byn) – PCxn
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