Abstract
We propose an extragradient method for solving equilibrium problems of pseudo-monotone type in Hadamard spaces. We prove \(\Delta \)-convergence of the generated sequence to a solution of the equilibrium problem, under standard assumptions on the bifunction. Then, we propose a regularization procedure which ensures strong convergence of the generated sequence to an equilibrium point of the problem.
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Acknowledgements
Research for this paper by the second author was supported by CNPq and IMPA. The second author is grateful to CNPq and IMPA for his post-doctoral scholarship.
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Communicated by Ernesto G. Birgin.
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Iusem, A.N., Mohebbi, V. Convergence analysis of the extragradient method for equilibrium problems in Hadamard spaces. Comp. Appl. Math. 39, 44 (2020). https://doi.org/10.1007/s40314-020-1076-1
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DOI: https://doi.org/10.1007/s40314-020-1076-1
Keywords
- Armijo-type search
- Equilibrium problem
- Extragradient method
- Halpern regularization
- Lipschitz continuous
- Pseudo-monotone bifunction