Modified extragradient algorithms for solving monotone variational inequalities and fixed point problems
Xiaopeng Zhao, Yonghong Yao
Abstract
In this paper, we investigate the monotone variational inequalities and fixed point problems in Hilbert spaces. Two modified extragradient algorithms are presented for finding a common element of the set of fixed points of a pseudocontractive operator and the set of solutions of the variational inequality problem. Weak and strong convergence of the suggested algorithms are proved.
Topics & Concepts
Variational inequalityMathematicsHilbert spaceMonotone polygonFixed pointConvergence (economics)Strongly monotoneOperator (biology)Set (abstract data type)Weak convergenceApplied mathematicsPoint (geometry)InequalityAlgorithmDiscrete mathematicsPure mathematicsMathematical analysisComputer scienceGeometryRepressorGeneProgramming languageBiochemistryComputer securityTranscription factorEconomicsEconomic growthAsset (computer security)ChemistryOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchTopology Optimization in Engineering