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
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
