Taiwanese Journal of Mathematics · 2009 · 19 citations · 10 references
Natural SciencesMathematicsComputational MechanicsFinite Element MethodsOptimizationConvergence AnalysisConvex AnalysisConvex OptimizationGradient-based OptimizationVariational InequalitiesWeak ConvergenceLipschitz ContinuityMonotone Variational InequalitiesNonexpansive MappingsVariational Inequality ProblemsVariational Inequality Theory
In this paper, we introduce a modified extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous mapping. Our modified extragradient method is a variant of the so-called extragradient method. We obtain a weak convergent theorem for two sequences generated by this modified extragradient method.
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