Abstract
In this paper, we introduce a modified relaxed projection algorithm and a modified variable-step relaxed projection algorithm for the split feasibility problem in infinite-dimensional Hilbert spaces. The weak convergence theorems under suitable conditions are proved. Finally, some numerical results are presented, which show the advantage of the proposed algorithms.
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Acknowledgments
The authors express their thanks to the reviewers, whose constructive suggestions led to improvements in the presentation of the results.
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Supported by the NSFC Tianyuan Youth Foundation of Mathematics of China (No. 11126136) and Fundamental Research Funds for the Central Universities (No. ZXH2011C002).
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Dong, QL., Yao, Y. & He, S. Weak convergence theorems of the modified relaxed projection algorithms for the split feasibility problem in Hilbert spaces. Optim Lett 8, 1031–1046 (2014). https://doi.org/10.1007/s11590-013-0619-4
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DOI: https://doi.org/10.1007/s11590-013-0619-4