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A novel method for hierarchical variational inequality with split common fixed point constraint

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Abstract

We address the strongly monotone variational inequality problem over the solution set of the split common fixed point problem with demimetric mappings in real Hilbert spaces. In order to solve this problem, we propose a new method that makes use of the inertial method with a correction term and a self-adaptive step size strategy. To demonstrate the effectiveness and performance of our proposed algorithm, we present two numerical examples, where one is related to the constrained convex minimization problem and the other is related to an application that performs binary classification based on support vector machines.

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Acknowledgements

The authors would like to dedicate this paper to Professor Ali Abkar on the occasion of his 60th birthday.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran

    Mohammad Eslamian & Ahmad Kamandi

Authors
  1. Mohammad Eslamian
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  2. Ahmad Kamandi
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Contributions

M.E. devised the project, the main conceptual ideas and proof outline. A.K. designed and performed the numerical experiments. All authors reviewed the results and approved the final version of the manuscript.

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Correspondence to Mohammad Eslamian.

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Eslamian, M., Kamandi, A. A novel method for hierarchical variational inequality with split common fixed point constraint. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02024-4

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