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Hybrid Splitting Methods for the System of Operator Inclusions with Monotone Operators1

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Cybernetics and Systems Analysis Aims and scope

Abstract

New algorithms are proposed to solve a system of operator inclusions with monotone operators acting in a Hilbert space. The algorithms are based on three well-known methods: the Tseng forward-backward splitting algorithm and two hybrid algorithms for approximation of fixed points of nonexpansive operators. Theorems on the strong convergence of the sequences generated by the algorithms are proved.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    V. V. Semenov

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  1. V. V. Semenov
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Correspondence to V. V. Semenov.

Additional information

1The study was sponsored by the Verkhovna Rada of Ukraine (the scholarship of the Verkhovna Rada of Ukraine for Young Scientists, 2013) and The State Fund for Fundamental Researches of Ukraine (Project GP/F49/061).

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2014, pp. 104–112.

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Semenov, V.V. Hybrid Splitting Methods for the System of Operator Inclusions with Monotone Operators1 . Cybern Syst Anal 50, 741–749 (2014). https://doi.org/10.1007/s10559-014-9664-y

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