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Strong convergence of a regularization method for Rockafellar’s proximal point algorithm

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Abstract

In this paper, for a monotone operator T, we shall show strong convergence of the regularization method for Rockafellar’s proximal point algorithm under more relaxed conditions on the sequences {r k } and {t k },

$$\lim\limits_{k\to\infty}t_k = 0;\quad \sum\limits_{k=0}^{+\infty}t_k = \infty;\quad\ \liminf\limits_{k\to\infty}r_k > 0.$$

Our results unify and improve some existing results.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xin Xiang, 453007, People’s Republic of China

    ChangAn Tian & Yisheng Song

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Yisheng Song

Authors
  1. ChangAn Tian
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  2. Yisheng Song
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Correspondence to ChangAn Tian or Yisheng Song.

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Tian, C., Song, Y. Strong convergence of a regularization method for Rockafellar’s proximal point algorithm. J Glob Optim 55, 831–837 (2013). https://doi.org/10.1007/s10898-011-9827-6

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  • DOI: https://doi.org/10.1007/s10898-011-9827-6

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