AN ACCELERATED HALPERN-TYPE ALGORITHM FOR SOLVING VARIATIONAL INCLUSION PROBLEMS WITH APPLICATIONS
Abubakar Adamu, Duangkamon Kitkuan, Thidaporn Seangwattana
2022Bangmod International Journal of Mathematical and Computational Science12 citationsDOIOpen Access PDF
Abstract
An inertial Halpern-type forward-backward iterative algorithm for approximating a zero of sum of two accretive operators is introduced and studied. Strong convergence theorem is established in a uniformly convex and q-uniformly smooth real Banach space. The convergence result obtained is applied to convex minimization and image restoration problems. Furthermore, numerical experiments are carried out on some classical test images and personal images degraded with motion blur and random noise. Finally, numerical illustrations in the Banach space, L5([−1, 1]) are presented to support the main theorem.
Topics & Concepts
Banach spaceMathematicsConvergence (economics)Type (biology)Regular polygonAlgorithmZero (linguistics)Applied mathematicsMathematical analysisMathematical optimizationGeometryPhilosophyLinguisticsEconomicsBiologyEconomic growthEcologySparse and Compressive Sensing TechniquesOptimization and Variational AnalysisNumerical methods in inverse problems