Tseng’s Algorithm with Extrapolation from the past Endowed with Variable Metrics and Error Terms
Buris Tongnoi
Abstract
In this paper, we propose a variable metric version of Tseng's algorithm (the forward-backward-forward algorithm: FBF) combined with extrapolation from the past that includes error terms for finding a zero of the sum of a maximally monotone operator and a monotone Lipschitzian operator in Hilbert spaces. The algorithm, which is a modified forward-reflected-backword method, is endowed with variable metrics and error terms. Primal-dual algorithms are also proposed for monotone inclusion problems involving compositions with linear operators. The primal-dual problem occurring in image deblurring demonstrates an application of our theoretical results.
Topics & Concepts
MathematicsExtrapolationMonotone polygonDeblurringHilbert spaceAlgorithmVariable (mathematics)Operator (biology)Metric (unit)Applied mathematicsZero (linguistics)Discrete mathematicsImage (mathematics)Pure mathematicsMathematical analysisImage processingImage restorationComputer scienceArtificial intelligenceGeneOperations managementEconomicsPhilosophyLinguisticsGeometryRepressorBiochemistryChemistryTranscription factorOptimization and Variational AnalysisSparse and Compressive Sensing TechniquesAdvanced Optimization Algorithms Research