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

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.

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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.

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Correspondence to Dang Van Hieu.

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Communicated by Hossein Mohebi.

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Van Hieu, D., Van Vy, L. & Quy, P.K. Three-operator splitting algorithm for a class of variational inclusion problems. Bull. Iran. Math. Soc. 46, 1055–1071 (2020). https://doi.org/10.1007/s41980-019-00312-5

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Keywords

  • Forward–backward method
  • Tseng’s method
  • Operator splitting method

Mathematics Subject Classification

  • 65J15
  • 47H05
  • 47J25
  • 47J20
  • 91B50