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An Inertial Iterative Regularization Method for a Class of Variational Inequalities

Author

Listed:
  • Nguyen Buong

    (Institute of Theoretical and Applied Research
    Duy Tan University
    Vietnam Academy of Science and Technology)

  • Nguyen Duong Nguyen

    (Foreign Trade University)

  • Nguyen Thi Quynh Anh

    (People’s Police University of Technology and Logistics)

Abstract

In this paper, we study a class of variational inequality problems the constraint set of which is the set of common solutions of a finite family of operator equations, involving hemi-continuous accretive operators on a reflexive and strictly convex Banach space with a Gâteaux differentiable norm. We present a sequential regularization method of Lavrentiev type and an iterative regularization one in combination with an inertial term to speed up convergence. The strong convergence of the methods is proved without the co-coercivity imposed on any operator in the family. An application of our results to solving the split common fixed point problem with pseudocontractive and nonexpansive operators is given with computational experiments for illustration.

Suggested Citation

  • Nguyen Buong & Nguyen Duong Nguyen & Nguyen Thi Quynh Anh, 2024. "An Inertial Iterative Regularization Method for a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 649-667, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02443-0
    DOI: 10.1007/s10957-024-02443-0
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    References listed on IDEAS

    as
    1. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
    2. Nguyen Buong & Lam Thuy Duong, 2011. "An Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 513-524, December.
    3. Nguyen Buong & Nguyen Thi Hong Phuong, 2013. "Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 399-411, November.
    4. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
    5. Haiyun Zhou & Peiyuan Wang, 2014. "A Simpler Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 716-727, June.
    6. Nguyen Buong, 2018. "Steepest†descent proximal point algorithms for a class of variational inequalities in Banach spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 291(8-9), pages 1191-1207, June.
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