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Forward-Backward Splitting with Bregman Distances

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Abstract

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces, where new algorithms are obtained.

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Acknowledgments

I would like to thank my doctoral advisor Professor Patrick L. Combettes for bringing this problem to my attention and for helpful discussions. The contributions of the referees to the article are important and I sincerely thank them for those.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay dist., Hanoi, Vietnam

    Quang Van Nguyen

  2. Laboratory for Information Theory and Inference Systems (LIONS), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Quang Van Nguyen

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  1. Quang Van Nguyen
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Correspondence to Quang Van Nguyen.

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Van Nguyen, Q. Forward-Backward Splitting with Bregman Distances. Vietnam J. Math. 45, 519–539 (2017). https://doi.org/10.1007/s10013-016-0238-3

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  • DOI: https://doi.org/10.1007/s10013-016-0238-3

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