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New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process

Author

Listed:
  • Andreea Bejenaru

    (Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Mihai Postolache

    (Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
    Business School, Sichuan University, Chengdu 610064, China
    Gh. Mihoc—C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania)

Abstract

Split variational inclusions are revealed as a large class of problems that includes several other pre-existing split-type issues: split feasibility, split zeroes problems, split variational inequalities and so on. This makes them not only a rich direction of theoretical study but also one with important and varied practical applications: large dimensional linear systems, optimization, signal reconstruction, boundary value problems and others. In this paper, the existing algorithmic tools are complemented by a new procedure based on a three-step iterative process. The resulting approximating sequence is proved to be weakly convergent toward a solution. The operation mode of the new algorithm is tracked in connection with mixed optimization–feasibility and mixed linear–feasibility systems. Standard polynomiographic techniques are applied for a comparative visual analysis of the convergence behavior.

Suggested Citation

  • Andreea Bejenaru & Mihai Postolache, 2022. "New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3617-:d:932367
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    References listed on IDEAS

    as
    1. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    2. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    3. Dianlu Tian & Lining Jiang & Luoyi Shi, 2019. "Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem," Mathematics, MDPI, vol. 7(10), pages 1-10, October.
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