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A Reflected Forward-Backward Splitting Method for Monotone Inclusions Involving Lipschitzian Operators

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Abstract

In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real Hilbert spaces. Applying the proposed method to composite monotone inclusions involving parallel sums yields a new primal-dual splitting which is different from the existing methods. Connections to existing works are clearly stated. We also provide an application of the proposed method to the image denoising by the total variation.

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Acknowledgments

We thank the referees for their suggestions and correction which helped to improve the first version of the manuscript. The work of B. Cong Vu and Volkan Cevher were supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no 725594 - time-data).

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Authors and Affiliations

  1. Laboratory for Information and Inference Systems, EPFL, Lausanne, Switzerland

    Volkan Cevher & Bằng Công Vũ

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  1. Volkan Cevher
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  2. Bằng Công Vũ
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Correspondence to Bằng Công Vũ.

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Cevher, V., Vũ, B.C. A Reflected Forward-Backward Splitting Method for Monotone Inclusions Involving Lipschitzian Operators. Set-Valued Var. Anal 29, 163–174 (2021). https://doi.org/10.1007/s11228-020-00542-4

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  • DOI: https://doi.org/10.1007/s11228-020-00542-4

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