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Received November 12, 2022; Accepted April 13, 2023; Published May 5, 2023
Abstract. In this paper, we study a split feasibility problem in Hilbert spaces. To solve the problem, Byrne introduced the extended CQ algorithm that involves the projections onto convex and closed subsets. However, the projections onto convex and closed subsets might be hard to be implemented in general. To overcome this difficulty, we propose a relaxed extended CQ algorithm in which the projections onto convex and closed subsets are replaced by the projections onto half-spaces. Under mild conditions, we establish the weak convergence of the proposed algorithm to a solution of the split feasibility problem.
How to Cite this Article:
W. Zhan, H. Yu, A relaxed extended CQ algorithm for the split feasibility problem in Hilbert spaces, J. Nonlinear Funct. Anal. 2023 (2023) 18.