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A Proximal Point Algorithm Revisited and Extended

Author

Listed:
  • Gheorghe Moroşanu

    (Academy of Romanian Scientists
    Babeş-Bolyai University)

  • Adrian Petruşel

    (Academy of Romanian Scientists
    Babeş-Bolyai University)

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.

Suggested Citation

  • Gheorghe Moroşanu & Adrian Petruşel, 2019. "A Proximal Point Algorithm Revisited and Extended," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1120-1129, September.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01536-5
    DOI: 10.1007/s10957-019-01536-5
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    References listed on IDEAS

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    1. Behzad Djafari Rouhani & Sirous Moradi, 2017. "Strong Convergence of Two Proximal Point Algorithms with Possible Unbounded Error Sequences," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 222-235, January.
    2. Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
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