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Some Remarks on the Proximal Point Algorithm

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Abstract

In this paper, we obtain some results on the boundedness and asymptotic behavior of the sequence generated by the proximal point algorithm without summability assumption on the error sequence. We also study the rate of convergence to minimum value of a proper, convex, and lower semicontinuous function. Finally, we consider the proximal point algorithm for solving equilibrium problems.

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Authors and Affiliations

  1. Department of Mathematics, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran

    Hadi Khatibzadeh

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  1. Hadi Khatibzadeh
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Correspondence to Hadi Khatibzadeh.

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Communicated by Nicolas Hadjisavvas.

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Khatibzadeh, H. Some Remarks on the Proximal Point Algorithm. J Optim Theory Appl 153, 769–778 (2012). https://doi.org/10.1007/s10957-011-9973-5

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  • DOI: https://doi.org/10.1007/s10957-011-9973-5

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