Abstract
Our aim in this paper is to study variants and computational errors of the extragradient method for solving equilibrium problems. First, we consider convergence of the method when domains in the auxiliary subproblems of the extragradient algorithm are replaced by outer and inner approximation polyhedra. Then, computational errors are showed under the asymptotic optimality condition, but the bifunction must satisfy certain Lipschitz-type continuous conditions. Next, by using Armijo-type linesearch techniques commonly used in variational inequalities, we obtain an approximation linesearch algorithm without Lipschitz continuity. Convergence analysis of the algorithms is considered under mild conditions on the iterative parameters.
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Acknowledgements
We are very grateful to the editor and anonymous referees for their comments that helped us very much in improving the paper. This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2017.15.
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Communicated by Norhashidah Hj. Mohd. Ali.
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Anh, P.N., Hien, N.D. & Tuan, P.M. Computational Errors of the Extragradient Method for Equilibrium Problems. Bull. Malays. Math. Sci. Soc. 42, 2835–2858 (2019). https://doi.org/10.1007/s40840-018-0632-y
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DOI: https://doi.org/10.1007/s40840-018-0632-y