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On the Strong Convergence of Halpern Type Proximal Point Algorithm

Author

Listed:
  • Hadi Khatibzadeh

    (University of Zanjan)

  • Sajad Ranjbar

    (University of Zanjan)

Abstract

The main result of this paper is to prove the strong convergence of the sequence generated by the proximal point algorithm of Halpern type to a zero of a maximal monotone operator under the suitable assumptions on the parameters and error. The results extend some of the previous results or give some different conditions for convergence of the sequence. It is also indicated that when the maximal monotone operator is the subdifferential of a convex, proper, and lower semicontinuous function, the results extend all previous results in the literature. We also prove the boundedness of the sequence generated by the algorithm with a weak coercivity condition defined in the paper and without any additional assumptions on the parameters.

Suggested Citation

  • Hadi Khatibzadeh & Sajad Ranjbar, 2013. "On the Strong Convergence of Halpern Type Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 385-396, August.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:2:d:10.1007_s10957-012-0213-4
    DOI: 10.1007/s10957-012-0213-4
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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. Hadi Khatibzadeh, 2012. "Some Remarks on the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 769-778, June.
    3. B. Djafari Rouhani & H. Khatibzadeh, 2008. "On the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 411-417, May.
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    Cited by:

    1. Vahid Dadashi & Mihai Postolache, 2017. "Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 518-529, August.

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