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Three-operator splitting algorithm for a class of variational inclusion problems

  • Dang Van HieuEmail author
  • Le Van Vy
  • Pham Kim Quy
Original Paper
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Abstract

This paper concerns with a new three-operator splitting algorithm for solving a class of variational inclusions. The main advantage of the proposed algorithm is that it can be easily implemented without the prior knowledge of Lipschitz constant, strongly monotone constant and cocoercive constant of component operators. A reason explained for this is that the algorithm uses a sequence of stepsizes which is diminishing and non-summable. The strong convergence of the algorithm is established. Several fundamental numerical experiments are given to illustrate the behavior of the new algorithm and compare it with other algorithms.

Keywords

Forward–backward method Tseng’s method Operator splitting method 

Mathematics Subject Classification

65J15 47H05 47J25 47J20 91B50 
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Notes

Acknowledgements

The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped us very much in improving the original version of this paper. The works of the first author are supported in part by the National Foundation for Science and Technology Development (NAFOS-TED) of Vietnam under Grant Number 101.01-2017.315.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Department of MathematicsCollege of Air ForceNha Trang CityVietnam

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