A Forward-Backward-Forward Algorithm for Solving Quasimonotone Variational Inequalities
Tzu-Chien Yin, Nawab Hussain
Abstract
In this paper, we continue to investigate the convergence analysis of Tseng-type forward-backward-forward algorithms for solving quasimonotone variational inequalities in Hilbert spaces. We use a self-adaptive technique to update the step sizes without prior knowledge of the Lipschitz constant of quasimonotone operators. Furthermore, we weaken the sequential weak continuity of quasimonotone operators to a weaker condition. Under some mild assumptions, we prove that Tseng-type forward-backward-forward algorithm converges weakly to a solution of quasimonotone variational inequalities.
Topics & Concepts
MathematicsLipschitz continuityVariational inequalityConvergence (economics)Type (biology)Applied mathematicsHilbert spaceConstant (computer programming)Mathematical analysisAlgorithmPure mathematicsComputer scienceEcologyEconomicsEconomic growthProgramming languageBiologyOptimization and Variational AnalysisContact Mechanics and Variational InequalitiesNumerical methods in inverse problems