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A new optimization approach to solving split equality problems in Hilbert spaces

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Abstract

We introduce a new optimization approach to solving systems of split equality problems in real Hilbert spaces. We use the inertial method in order to improve the convergence rate of the proposed algorithms. Our algorithms do not depend on the norms of the bounded linear operators which appear in each split equality problem of the system under consideration. This is also a strong point of our algorithms because it is known that it is difficult to compute or estimate the norm of a linear operator in the general case.

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Acknowledgements

All the authors are grateful to the editors and to an anonymous referee for their useful comments and helpful suggestions.

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion (Grant 2001893) and by the Technion General Research Fund (Grant 2016723). Truong Minh Tuyen and Nguyen Song Ha were supported by the Science and Technology Fund of the Thai Nguyen University of Sciences.

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Authors and Affiliations

  1. Department of Mathematics, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich

  2. Thainguyen University of Sciences, Thainguyen, Vietnam

    Truong Minh Tuyen & Nguyen Song Ha

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  1. Simeon Reich
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  2. Truong Minh Tuyen
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  3. Nguyen Song Ha
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All authors wrote the main manuscript text and reviewed the manuscript.

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Correspondence to Truong Minh Tuyen or Nguyen Song Ha.

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Reich, S., Tuyen, T.M. & Ha, N.S. A new optimization approach to solving split equality problems in Hilbert spaces. J Glob Optim (2024). https://doi.org/10.1007/s10898-024-01389-x

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