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On the contraction-proximal point algorithms with multi-parameters

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  • Fenghui Wang
  • Huanhuan Cui

Abstract

In this paper we consider the contraction-proximal point algorithm: $${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$$ where $${J_{\beta_n}}$$ denotes the resolvent of a monotone operator A. Under the assumption that lim n α n = 0, ∑ n α n = ∞, lim inf n β n > 0, and lim inf n γ n > 0, we prove the strong convergence of the iterates as well as its inexact version. As a result we improve and recover some recent results by Boikanyo and Morosanu. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:485-491
    DOI: 10.1007/s10898-011-9772-4
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    References listed on IDEAS

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    1. O. Boikanyo & G. Moroşanu, 2011. "Inexact Halpern-type proximal point algorithm," Journal of Global Optimization, Springer, vol. 51(1), pages 11-26, September.
    2. Fenghui Wang, 2011. "A note on the regularized proximal point algorithm," Journal of Global Optimization, Springer, vol. 50(3), pages 531-535, July.
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    Citations

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    Cited by:

    1. Gheorghe Moroşanu & Adrian Petruşel, 2019. "A Proximal Point Algorithm Revisited and Extended," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1120-1129, September.
    2. Yamin Wang & Fenghui Wang & Hong-Kun Xu, 2016. "Error Sensitivity for Strongly Convergent Modifications of the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 901-916, March.
    3. Cui, Huanhuan & Su, Menglong, 2015. "On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 67-71.
    4. Peeyada, Pronpat & Suparatulatorn, Raweerote & Cholamjiak, Watcharaporn, 2022. "An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. Prasit Cholamjiak & Suparat Kesornprom & Nattawut Pholasa, 2019. "Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    6. Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
    7. J. H. Wang & C. Li & J.-C. Yao, 2015. "Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 188-212, July.

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