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New self-adaptive step size algorithms for solving split variational inclusion problems and its applications

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Abstract

In this paper, we study a special instance of the split inverse problem (SIP), which is the split variational inclusion problem (SVIP). Three simple iterative methods for solving it are introduced and weak and strong convergence theorems are established under mild and standard assumptions. As an application, the problem of minimizing two proper, convex, and lower semi-continuous functions is considered. We compare and illustrate the efficiency and applicability of our schemes for several numerical experiments as well as an example in the field of compressed sensing.

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Acknowledgments

The authors express their deep gratitude to the referee and the editor for his/her valuable comments and suggestions.

Funding

This work was supported by the National Natural Science Foundation of China (11471059) and the Science and Technology Research Project of Chongqing Municipal Education Commission (KJ 1706154) and the Research Project of Chongqing Technology and Business University (KFJJ2017069).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Yan Tang

  2. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing, 400067, China

    Yan Tang

  3. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

  4. The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, 3498838, Haifa, Israel

    Aviv Gibali

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  1. Yan Tang
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  2. Aviv Gibali
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Correspondence to Yan Tang.

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Tang, Y., Gibali, A. New self-adaptive step size algorithms for solving split variational inclusion problems and its applications. Numer Algor 83, 305–331 (2020). https://doi.org/10.1007/s11075-019-00683-0

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