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Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces

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Abstract

The split feasibility problem is to find a point x∗ with the property that x∗∈ C and Ax∗∈ Q, where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y, respectively, and A is a bounded linear operator from X to Y. The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce a new inertial relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposed CQ algorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem.

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Funding

The third author was supported by Open Fund of Tianjin Key Lab for Advanced Signal Processing (No. 2016ASP-TJ01).

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    D.R. Sahu & M.R. Kashyap

  2. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Y.J. Cho

  3. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Y.J. Cho

  4. Key Laboratory for Advanced Signal Processing and College of Science, Civil Aviation University of China, Tianjin, 300300, People’s Republic of China

    Q.L. Dong & X.H. Li

Authors
  1. D.R. Sahu
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  2. Y.J. Cho
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  3. Q.L. Dong
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  4. M.R. Kashyap
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  5. X.H. Li
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Correspondence to Q.L. Dong.

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Sahu, D., Cho, Y., Dong, Q. et al. Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces. Numer Algor 87, 1075–1095 (2021). https://doi.org/10.1007/s11075-020-00999-2

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  • DOI: https://doi.org/10.1007/s11075-020-00999-2

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