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Regularization Proximal Method for Monotone Variational Inclusions

Author

Listed:
  • Dang Hieu

    (TIMAS - Thang Long University)

  • Pham Ky Anh

    (Vietnam National University)

  • Nguyen Hai Ha

    (University of Transport and Communications)

Abstract

The paper concerns with a new iterative method for solving a monotone variational inclusion problem in a Hilbert space. The method is of the proximal contraction type incorporated with the regularization technique. Under the prediction stepsize conditions, we establish the strong convergence of the iterative sequences generated by the method to a particular solution of the problem satisfying a variational inequality problem. Finally, we give some numerical examples to illustrate the behavior of the new method in comparison with existing ones.

Suggested Citation

  • Dang Hieu & Pham Ky Anh & Nguyen Hai Ha, 2021. "Regularization Proximal Method for Monotone Variational Inclusions," Networks and Spatial Economics, Springer, vol. 21(4), pages 905-932, December.
    • Handle: RePEc:kap:netspa:v:21:y:2021:i:4:d:10.1007_s11067-021-09552-7
    DOI: 10.1007/s11067-021-09552-7
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    References listed on IDEAS

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    1. Martin Seydenschwanz, 2015. "Convergence results for the discrete regularization of linear-quadratic control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 61(3), pages 731-760, July.
    2. 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.
    3. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
    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.
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