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A Splitting Algorithm for System of Composite Monotone Inclusions

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Abstract

We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resulting algorithm is an extension of the algorithm in Becker and Combettes (J. Convex Nonlinear Anal. 15, 137–159, 2014). The weak convergence of the algorithm proposed is proved. Applications to minimization problems is demonstrated.

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Notes

  1. SNR between an image y and the original image \(\overline {y}\) is defined as \(20\log _{10}(\|\overline {y}\|/\|y-\overline {y}\|)\).

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Acknowledgments

This work is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 102.01-2014.02. A part of the research work of Dinh Dũng was done when the author was working as a research professor at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for providing a fruitful research environment and working condition. We thank the referees for their suggestions and corrections which helped to improve the first version of the manuscript.

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Authors and Affiliations

  1. Information Technology Institute, Vietnam National University, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Dinh Dũng

  2. Department of Mathematics, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Bằng Công Vũ

Authors
  1. Dinh Dũng
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  2. Bằng Công Vũ
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Correspondence to Bằng Công Vũ.

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Dedicated to the 65th birthday of Professor Nguyen Khoa Son.

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Dũng, D., Vũ, B.C. A Splitting Algorithm for System of Composite Monotone Inclusions. Vietnam J. Math. 43, 323–341 (2015). https://doi.org/10.1007/s10013-015-0121-7

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  • DOI: https://doi.org/10.1007/s10013-015-0121-7

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