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

  • Authors:

  • Changan Tian;Yisheng Song

  • Affiliations:

  • College of Mathematics and Information Science, Henan Normal University, Xin Xiang, People's Republic of China 453007;College of Mathematics and Information Science, Henan Normal University, Xin Xiang, People's Republic of China 453007 and Department of Applied Mathematics, The Hong Kong Polytechnic University, H ...

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2013

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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.