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

  • Pham Ky Anh
  • Nguyen The Vinh
  • Vu Tien Dung


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.


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

Mathematics Subject Classification

Primary 47J25 Secondary 65K15 



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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics, Mechanics, and InformaticsVietnam National UniversityHanoiVietnam
  2. 2.Department of MathematicsUniversity of Transport and CommunicationsHanoiVietnam

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