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New iterative algorithms for solving split variational inclusions

Author

Listed:
  • Soumitra Dey

    (The Technion- Israel Institute of Technology
    University of Haifa)

  • Chinedu Izuchukwu

    (University of the Witwatersrand)

  • Adeolu Taiwo

    (The Technion- Israel Institute of Technology)

  • Simeon Reich

    (The Technion- Israel Institute of Technology)

Abstract

In this paper we study a class of split variational inclusion (SVI) and regularized split variational inclusion (RSVI) problems in real Hilbert spaces. We discuss various analytical properties of the net generated by the RSVI and establish the existence and uniqueness of the solution to the RSVI. Using analytical properties of this net and under certain assumptions on the parameters and mappings associated with the SVI, we establish the strong convergence of the sequence generated by our proposed iterative algorithm. We also deduce another iterative algorithm by taking the regularization parameters to be zero in our proposed algorithm. We establish the weak convergence of the sequence generated by our new algorithm under certain assumptions. Moreover, we discuss two special cases of the SVI, namely the split convex minimization and the split variational inequality problems, and give several numerical examples.

Suggested Citation

  • Soumitra Dey & Chinedu Izuchukwu & Adeolu Taiwo & Simeon Reich, 2025. "New iterative algorithms for solving split variational inclusions," Journal of Global Optimization, Springer, vol. 91(3), pages 587-609, March.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:3:d:10.1007_s10898-024-01444-7
    DOI: 10.1007/s10898-024-01444-7
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    References listed on IDEAS

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    1. Ferdinard U. Ogbuisi & Yekini Shehu & Jen-Chih Yao, 2023. "Relaxed Single Projection Methods for Solving Bilevel Variational Inequality Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(3), pages 641-678, September.
    2. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    3. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    4. Xingju Cai & Guoyong Gu & Bingsheng He, 2014. "On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators," Computational Optimization and Applications, Springer, vol. 57(2), pages 339-363, March.
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