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A Relaxed Forward-Backward-Forward Algorithm with Alternated Inertial Step: Weak and Linear Convergence

Author

Listed:
  • Yekini Shehu

    (Zhejiang Normal University)

  • Lulu Liu

    (Civil Aviation University of China)

  • Qiao-Li Dong

    (Civil Aviation University of China)

  • Jen-Chih Yao

    (China Medical University)

Abstract

We study the forward-backward-forward splitting method with alternated inertial step in this paper. We consider under-relaxation and over-relaxation approaches to the proposed method and obtain weak convergence results in both cases in real Hilbert spaces. Linear convergence alongside priori and apriori error estimates are obtained under some standard assumptions. Finally, we give some numerical implementations and comparisons to support the theoretical analysis.

Suggested Citation

  • Yekini Shehu & Lulu Liu & Qiao-Li Dong & Jen-Chih Yao, 2022. "A Relaxed Forward-Backward-Forward Algorithm with Alternated Inertial Step: Weak and Linear Convergence," Networks and Spatial Economics, Springer, vol. 22(4), pages 959-990, December.
    • Handle: RePEc:kap:netspa:v:22:y:2022:i:4:d:10.1007_s11067-022-09575-8
    DOI: 10.1007/s11067-022-09575-8
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    References listed on IDEAS

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    1. Puya Latafat & Panagiotis Patrinos, 2017. "Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators," Computational Optimization and Applications, Springer, vol. 68(1), pages 57-93, September.
    2. Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
    3. J. Preininger & P. T. Vuong, 2018. "On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 70(1), pages 221-238, May.
    4. Tran Quoc & Pham Anh & Le Muu, 2012. "Dual extragradient algorithms extended to equilibrium problems," Journal of Global Optimization, Springer, vol. 52(1), pages 139-159, January.
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