A Modified Tseng's Algorithm with Extrapolation from the Past for Pseudo-monotone Variational Inequalities
Buris Tongnoi
Abstract
We present Tseng's forward-backward-forward method with extrapolation from the past for pseudo-monotone variational inequalities in Hilbert spaces. In addition, we propose a variable stepsize scheme of the extrapolated Tseng's algorithm governed by the operator which is pseudo-monotone, Lipschitz continuous and sequentially weak-to-weak continuous. We also investigate the algorithm's adaptive stepsize scenario, which arises when it is impossible to calculate the Lipschitz constant of a pseudo-monotone operator correctly. Finally, we prove a weak convergence theorem and conduct a numerical experiment to support it.
Topics & Concepts
MathematicsLipschitz continuityMonotone polygonExtrapolationVariational inequalityHilbert spaceConvergence (economics)Strongly monotoneConstant (computer programming)Operator (biology)Applied mathematicsWeak convergenceAlgorithmMathematical analysisComputer scienceComputer securityGeometryEconomicsGeneTranscription factorChemistryRepressorProgramming languageEconomic growthAsset (computer security)BiochemistryOptimization and Variational AnalysisContact Mechanics and Variational InequalitiesNumerical methods in inverse problems