Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces
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In this paper we are focused on solving monotone and Lipschitz continuous variational inequalities in real Hilbert spaces. Motivated by several recent results related to the subgradient extragradient method (SEM), we propose two SEM extensions which do not require the knowledge of the Lipschitz constant associated with the variational inequality operator. Under mild and standard conditions, we establish the strong convergence of our schemes. Primary numerical examples demonstrate the potential of our algorithms as well as compare their performances to several related results.
KeywordsProjection and contraction method Subgradient extragradient method Mann type method Viscosity method Variational inequality problem
Mathematics Subject Classification47H09 47H10 47J20 47J25
The authors would like to thank the referees for their comments on the manuscript which helped in improving earlier version of this paper.
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