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Convergence analysis for the proximal split feasibility problem using an inertial extrapolation term method

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Abstract

In this paper, we present a proximal split feasibility algorithm with an additional inertial extrapolation term for solving a proximal split feasibility problem under weaker conditions on the step sizes. The two convex and lower semi continuous objective functions are assumed to be non-smooth. Some applications to split inclusion problem and split equilibrium problem are given. We demonstrate the efficiency of the proposed algorithm with numerical experiments.

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Acknowledgements

The research was carried out when the First 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.

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Authors and Affiliations

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

    Yekini Shehu

  2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Wisconsin, USA

    Olaniyi S. Iyiola

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  1. Yekini Shehu
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  2. Olaniyi S. Iyiola
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Correspondence to Yekini Shehu.

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Y. Shehu is currently an Alexander von Humboldt Postdoctoral Fellow at the Institute of Mathematics, University of Wurzburg, Germany.

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Shehu, Y., Iyiola, O.S. Convergence analysis for the proximal split feasibility problem using an inertial extrapolation term method. J. Fixed Point Theory Appl. 19, 2483–2510 (2017). https://doi.org/10.1007/s11784-017-0435-z

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