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Some Remarks on the Proximal Point Algorithm

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  • Hadi Khatibzadeh

    (University of Zanjan)

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.

Suggested Citation

  • Hadi Khatibzadeh, 2012. "Some Remarks on the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 769-778, June.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-011-9973-5
    DOI: 10.1007/s10957-011-9973-5
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    References listed on IDEAS

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    1. 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.
    2. 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.

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