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An explicit extragradient algorithm for equilibrium problems on Hadamard manifolds

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Abstract

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.

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Acknowledgements

The authors are grateful to the referees for the valuable comments which improved the presentation of this paper.

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Correspondence to Jingjing Fan.

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Communicated by Joerg Fliege.

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Fan, J., Tan, B. & Li, S. An explicit extragradient algorithm for equilibrium problems on Hadamard manifolds. Comp. Appl. Math. 40, 68 (2021). https://doi.org/10.1007/s40314-021-01427-4

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