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Inertial forward-backward splitting method in Banach spaces with application to compressed sensing

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Abstract

We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the lew available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.

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Acknowledgements

We are sincerely grateful to the Editor and the anonymous reviewer for comments and suggestions which have improved the original manuscript greatly.

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Authors and Affiliations

  1. School of Science, University of Phayao, 19 Moo 2 Tambon Maeka Amphur Muang, Phayao, 56000, Thailand

    Prasit Cholamjiak

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

    Yekini Shehu

Authors
  1. Prasit Cholamjiak
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  2. Yekini Shehu
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Corresponding author

Correspondence to Yekini Shehu.

Additional information

P. Cholamjiak is supported by the Thailand Research Fund and the University of Phayao under grant RSA6180084. The research of the second author is supported by the Alexander von Humboldt-Foundation.

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Cholamjiak, P., Shehu, Y. Inertial forward-backward splitting method in Banach spaces with application to compressed sensing. Appl Math 64, 409–435 (2019). https://doi.org/10.21136/AM.2019.0323-18

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