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A strong convergence result involving an inertial forward–backward algorithm for monotone inclusions

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Abstract

Our interest in this paper is to prove a strong convergence result for finding a zero of the sum of two monotone operators, with one of the two operators being co-coercive using an iterative method which is a combination of Nesterov’s acceleration scheme and Haugazeau’s algorithm in real Hilbert spaces. Our numerical results show that the proposed algorithm converges faster than the un-accelerated Haugazeau’s algorithm.

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Acknowledgements

The research was carried out when the Fourth Author was an Alexander von Humboldt Postdoctoral Fellow at the Institute of Mathematics, University of Wurzburg, Germany. He is grateful to the Alexander von Humboldt Foundation, Bonn, for the fellowship and the Institute of Mathematics, Julius Maximilian University of Wurzburg, Germany for the hospitality and facilities. P. Cholamjiak was supported by the Thailand Research Fund and the Commission on Higher Education under Grant MRG5980248.

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  1. Yekini Shehu

    Present address: Institute of Mathematics, University of Wurzburg, Würzburg, Germany

Authors and Affiliations

  1. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiaoli Dong & Dan Jiang

  2. School of Science, University of Phayao, Phayao, 56000, Thailand

    Prasit Cholamjiak

  3. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

    Yekini Shehu

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  1. Qiaoli Dong
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Dong, Q., Jiang, D., Cholamjiak, P. et al. A strong convergence result involving an inertial forward–backward algorithm for monotone inclusions. J. Fixed Point Theory Appl. 19, 3097–3118 (2017). https://doi.org/10.1007/s11784-017-0472-7

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