Journal
NUMERICAL ALGORITHMS
Volume 92, Issue 2, Pages 1335-1366Publisher
SPRINGER
DOI: 10.1007/s11075-022-01343-6
Keywords
Split feasibility problem; Split feasibility problem with multiple output sets; Hilbert space; Relaxed CQ algorithm; Self-adaptive technique
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In this paper, we study the split feasibility problem with multiple output sets in Hilbert spaces. We propose two new self-adaptive relaxed CQ algorithms which involve computing of projections onto half-spaces instead of computing onto the closed convex sets, and it does not require calculating the operator norm. We establish a weak and a strong convergence theorems for the proposed algorithms. We apply the new results to solve some other problems. Finally, we present some numerical examples to show the efficiency and accuracy of our algorithm compared to some existing results. Our results extend and improve some existing methods in the literature.
In this paper, we study the split feasibility problem with multiple output sets in Hilbert spaces. For solving the aforementioned problem, we propose two new self-adaptive relaxed CQ algorithms which involve computing of projections onto half-spaces instead of computing onto the closed convex sets, and it does not require calculating the operator norm. We establish a weak and a strong convergence theorems for the proposed algorithms. We apply the new results to solve some other problems. Finally, we present some numerical examples to show the efficiency and accuracy of our algorithm compared to some existing results. Our results extend and improve some existing methods in the literature.
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