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A Proximal Point Algorithm Revisited and Extended

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Abstract

This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222–235, 2017), where a proximal point algorithm proposed by Boikanyo and Moroşanu (Optim Lett 7:415–420, 2013) is discussed. Noticing the inappropriate formulation of that algorithm, we propose a more general algorithm for approximating zeros of a maximal monotone operator on a Hilbert space. Besides the main result on the strong convergence of the sequences generated by this new algorithm, we discuss some particular cases, including the approximation of minimizers of convex functionals and present two examples to illustrate the applicability of the algorithm. The note clarifies and extends both the papers quoted above.

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Acknowledgements

Many thanks are due to the editor and reviewers for comments and useful suggestions.

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Authors and Affiliations

  1. Academy of Romanian Scientists, Bucharest, Romania

    Gheorghe Moroşanu & Adrian Petruşel

  2. Babeş-Bolyai University, Cluj-Napoca, Romania

    Gheorghe Moroşanu & Adrian Petruşel

Authors
  1. Gheorghe Moroşanu
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  2. Adrian Petruşel
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Correspondence to Gheorghe Moroşanu.

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Moroşanu, G., Petruşel, A. A Proximal Point Algorithm Revisited and Extended. J Optim Theory Appl 182, 1120–1129 (2019). https://doi.org/10.1007/s10957-019-01536-5

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  • DOI: https://doi.org/10.1007/s10957-019-01536-5

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