A new self-adaptive CQ algorithm with an application to the LASSO problem

Abstract

In this paper, we introduce a new self-adaptive CQ algorithm for solving split feasibility problems in real Hilbert spaces. The algorithm is designed, such that the stepsizes are directly computed at each iteration. We also consider the corresponding relaxed CQ algorithm for the proposed method. Under certain mild conditions, we establish weak convergence of the proposed algorithm as well as strong convergence of its hybrid-type variant. Finally, numerical examples illustrating the efficiency of our algorithm in solving the LASSO problem are presented.

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Acknowledgements

The authors would like to thank the editor and the reviewers for their constructive suggestions and comments, which greatly improve the manuscript.

The second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No.101.01-2017.08. His research is also partially supported by the Vietnam Institute for Advanced Study in Mathematics and by UTC under Grant T2018-CB-002.

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Correspondence to Nguyen The Vinh.

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Anh, P.K., Vinh, N.T. & Dung, V.T. A new self-adaptive CQ algorithm with an application to the LASSO problem. J. Fixed Point Theory Appl. 20, 142 (2018). https://doi.org/10.1007/s11784-018-0620-8

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Keywords

  • Split feasibility problem
  • variational inequality
  • fixed point problem
  • monotone operator
  • weak convergence
  • strong convergence

Mathematics Subject Classification

  • Primary 47J25
  • Secondary 65K15