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An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems

Author

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  • Tianle Lu

    (School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China)

  • Xue Zhang

    (School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China)

Abstract

In this paper, we propose an inertial parametric Douglas–Rachford splitting method for minimizing the sum of two nonconvex functions, which has a wide range of applications. The proposed algorithm combines the inertial technique, the parametric technique, and the Douglas–Rachford method. Subsequently, in theoretical analysis, we construct a new merit function and establish the convergence of the sequence generated by the inertial parametric Douglas–Rachford splitting method. Finally, we present some numerical results on nonconvex feasibility problems to illustrate the efficiency of the proposed method.

Suggested Citation

  • Tianle Lu & Xue Zhang, 2024. "An Inertial Parametric Douglas–Rachford Splitting Method for Nonconvex Problems," Mathematics, MDPI, vol. 12(5), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:675-:d:1345769
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    References listed on IDEAS

    as
    1. Dongying Wang & Xianfu Wang, 2019. "A parameterized Douglas–Rachford algorithm," Computational Optimization and Applications, Springer, vol. 73(3), pages 839-869, July.
    2. 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.
    3. Minh N. Dao, & Hung M. Phan, 2019. "Linear Convergence of Projection Algorithms," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 715-738, May.
    4. Guoyin Li & Tianxiang Liu & Ting Kei Pong, 2017. "Peaceman–Rachford splitting for a class of nonconvex optimization problems," Computational Optimization and Applications, Springer, vol. 68(2), pages 407-436, November.
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