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A generalized scheme for split inclusion problem with conjugate like direction

Author

Listed:
  • Jamilu Abubakar

    (King Mongkut’s University of Technology Thonburi
    Usmanu Danfodiyo University Sokoto)

  • Parin Chaipunya

    (King Mongkut’s University of Technology Thonburi)

  • Poom Kumam

    (King Mongkut’s University of Technology Thonburi)

  • Sani Salisu

    (King Mongkut’s University of Technology Thonburi)

Abstract

This paper, we propose enhanced methods for solving the generalized split inclusion problem involving several maximally monotone operators. The proposed algorithms incorporate conjugate gradient methods technique, in particular, the conjugate direction approach into the CQ algorithm. We showed that the sequences generated by the proposed methods converges strongly under mild conditons. Additionally, we present numerical illustrations to demonstrate the convergence of the sequence generated by the proposed methods, validate our theoretical findings and showcase the computational performance of the proposed method.

Suggested Citation

  • Jamilu Abubakar & Parin Chaipunya & Poom Kumam & Sani Salisu, 2025. "A generalized scheme for split inclusion problem with conjugate like direction," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(1), pages 51-71, February.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:1:d:10.1007_s00186-024-00882-z
    DOI: 10.1007/s00186-024-00882-z
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    References listed on IDEAS

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    1. Che, Haitao & Li, Meixia, 2016. "The conjugate gradient method for split variational inclusion and constrained convex minimization problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 426-438.
    2. Fenghui Wang, 2022. "The Split Feasibility Problem with Multiple Output Sets for Demicontractive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 837-853, December.
    3. Simeon Reich & Truong Minh Tuyen, 2020. "Two Projection Algorithms for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 148-168, July.
    4. Qiao-Li Dong & Yeol Je Cho & Themistocles M. Rassias, 2018. "General Inertial Mann Algorithms and Their Convergence Analysis for Nonexpansive Mappings," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Applications of Nonlinear Analysis, pages 175-191, Springer.
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