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Accelerated hybrid methods for solving pseudomonotone equilibrium problems

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Abstract

In this paper, we introduce some new accelerated hybrid algorithms for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition in a Hilbert space. The algorithms are constructed around the extragradient method, the inertial technique, the hybrid (or outer approximation) method, and the shrinking projection method. The algorithms are designed to work either with or without the prior knowledge of the Lipschitz-type constants of bifunction. Theorems of strong convergence are established under mild conditions. The results in this paper generalize, extend, and improve some known results in the field. Finally, several of numerical experiments are performed to support the obtained theoretical results.

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Acknowledgments

The authors would like to thank the Editor and the referees for their comments on the manuscript which helped in improving earlier version of this paper.

Funding

The first author was financially supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2020.06.

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Correspondence to Dang Van Hieu.

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Communicated by: Russell Luke

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Van Hieu, D., Quy, P.K., Hong, L.T. et al. Accelerated hybrid methods for solving pseudomonotone equilibrium problems. Adv Comput Math 46, 58 (2020). https://doi.org/10.1007/s10444-020-09778-y

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