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Modified Alternating Direction Methods for the Modified Multiple-Sets Split Feasibility Problems

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Abstract

In this paper, we propose two new multiple-sets split feasibility problem models and new solution methods. The first model is more separable than the original one, which enables us to apply a modified alternating direction method with parallel steps to solve it. Then, to overcome the difficulty of computing projections onto the constraint sets, a special version of this modified method with the strategy of projection onto half-space is given. The second model consists in finding a least Euclidean norm solution of the multiple-sets split feasibility problem, for which we provide another modified alternating direction method. Numerical results presented at the last show the efficiency of our methods.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (Grant No. 11271206) and Fundamental Research Funds for the Central Universities (Grant No. NKZXB10089). The authors thank the editor and the anonymous referees for their careful reading of the paper and valuable comments.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P.R. China

    Yuning Yang & Qingzhi Yang

  2. Business School and China Academy of Corporate Governance, Nankai University, Tianjin, 300071, P.R. China

    Su Zhang

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  1. Yuning Yang
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  2. Qingzhi Yang
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  3. Su Zhang
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Correspondence to Su Zhang.

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Yang, Y., Yang, Q. & Zhang, S. Modified Alternating Direction Methods for the Modified Multiple-Sets Split Feasibility Problems. J Optim Theory Appl 163, 130–147 (2014). https://doi.org/10.1007/s10957-013-0502-6

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  • DOI: https://doi.org/10.1007/s10957-013-0502-6

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