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A Proximal Point Algorithm Revisited and Extended

  • Gheorghe MoroşanuEmail author
  • Adrian Petruşel
Regular Paper
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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.

Keywords

Maximal monotone operator Proximal point algorithm Strong convergence Convex function 

Mathematics Subject Classification

47J25 47H05 90C25 90C90 

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Academy of Romanian ScientistsBucharestRomania
  2. 2.Babeş-Bolyai UniversityCluj-NapocaRomania

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