A strong convergence theorem for Tseng’s extragradient method for solving variational inequality problems
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In this paper, we introduce a new algorithm for solving variational inequality problems with monotone and Lipschitz-continuous mappings in real Hilbert spaces. Our algorithm requires only to compute one projection onto the feasible set per iteration. We prove under certain mild assumptions, a strong convergence theorem for the proposed algorithm to a solution of a variational inequality problem. Finally, we give some numerical experiments illustrating the performance of the proposed algorithm for variational inequality problems.
KeywordsTseng’s extragradient Viscosity method Variational inequality problem
The authors would like to two anonymous reviewers for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper. This paper was completed when the first two authors were visiting the Vietnam Institute for Advance Study in Mathematics (VIASM) and they thank the VIASM for financial support and hospitality and the second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No.101.01-2017.08.
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