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Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery

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Abstract

In this paper, we study the bounded perturbation resilience of projection and contraction algorithms for solving variational inequality (VI) problems in real Hilbert spaces. Under typical and standard assumptions of monotonicity and Lipschitz continuity of the VI’s associated mapping, convergence of the perturbed projection and contraction algorithms is proved. Based on the bounded perturbed resilience of projection and contraction algorithms, we present some inertial projection and contraction algorithms. In addition, we show that the perturbed algorithms converge at the rate of O(1 / t).

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Acknowledgements

We wish to thank the anonymous referees for the thorough analysis and review, their comments and suggestions helped tremendously in improving the quality of this paper and made it suitable for publication. The first author is supported by the National Natural Science Foundation of China (No. 71602144) and Open Fund of Tianjin Key Lab for Advanced Signal Processing (No. 2016ASP-TJ01). The second author is supported by the EU FP7 IRSES program STREVCOMS (No. PIRSES-GA-2013-612669).

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Authors and Affiliations

  1. Tianjin Key Laboratory for Advanced Signal Processing, College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong, Dan Jiang & Shang-Hong Ke

  2. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

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  1. Qiao-Li Dong
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  2. Aviv Gibali
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  3. Dan Jiang
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  4. Shang-Hong Ke
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Correspondence to Aviv Gibali.

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Dong, QL., Gibali, A., Jiang, D. et al. Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery. J. Fixed Point Theory Appl. 20, 16 (2018). https://doi.org/10.1007/s11784-018-0501-1

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  • DOI: https://doi.org/10.1007/s11784-018-0501-1

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