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Iterative method with inertial terms for nonexpansive mappings: applications to compressed sensing

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Abstract

Our interest in this paper is to introduce a Halpern-type algorithm with both inertial terms and errors for approximating fixed point of a nonexpansive mapping. We obtain strong convergence of the sequence generated by our proposed method in real Hilbert spaces under some reasonable assumptions on the sequence of parameters. As applications, we present some strong convergence results for monotone inclusion, variational inequality problem, linear inverse problem, and LASSO problem in Compressed Sensing. Our result improves the rate of convergence of existing Halpern method for monotone inclusion, variational inequality problem, linear inverse problem and LASSO problem in compressed sensing as illustrated in our numerical examples both in finite and infinite dimensional Hilbert spaces.

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Acknowledgments

The research of Y. Shehu is supported by the Alexander von Humboldt-Foundation and Postdoctoral Fellowship from the Institute of Science and Technology (IST), Klosterneuburg, Vienna, Austria.

The research of F. U. Ogbuisi is wholly supported by the National Research Foundation (NRF) of South Africa (S& F-DST/NRF Innovation Postdoctoral Fellowship; Grant Number: 111992). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

  2. Department of Mathematics, Computer Science and Information System, California University of Pennsylvania, California, PA, USA

    Olaniyi S. Iyiola

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

    Ferdinard U. Ogbuisi

  4. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    Ferdinard U. Ogbuisi

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  1. Yekini Shehu
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Shehu, Y., Iyiola, O.S. & Ogbuisi, F.U. Iterative method with inertial terms for nonexpansive mappings: applications to compressed sensing. Numer Algor 83, 1321–1347 (2020). https://doi.org/10.1007/s11075-019-00727-5

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