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Strong convergence of a splitting projection method for the sum of maximal monotone operators

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Abstract

In this paper, a projective-splitting method is proposed for finding a zero of the sum of \(n\) maximal monotone operators over a real Hilbert space \(\mathcal{H }\). Without the condition that either \(\mathcal{H }\) is finite dimensional or the sum of \(n\) operators is maximal monotone, we prove that the sequence generated by the proposed method is strongly convergent to an extended solution for the problem, which is closest to the initial point. The main results presented in this paper generalize and improve some recent results in this topic.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (10671135), the Doctoral Fund of Ministry of Education of China (20105134120002), the Application Foundation Fund of Sichuan Technology Department of China (2010JY0121), the Key of Chinese Ministry of Education (212147)

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Authors and Affiliations

  1. School of Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, People’s Republic of China

    Guo-ji Tang

  2. Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, 610068, People’s Republic of China

    Fu-quan Xia

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  1. Guo-ji Tang
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  2. Fu-quan Xia
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Correspondence to Fu-quan Xia.

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Tang, Gj., Xia, Fq. Strong convergence of a splitting projection method for the sum of maximal monotone operators. Optim Lett 8, 1313–1324 (2014). https://doi.org/10.1007/s11590-013-0649-y

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  • DOI: https://doi.org/10.1007/s11590-013-0649-y

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