Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Feasibility and Infeasibility in Optimization: Algorithms and Computational Methods
Feasibility and Infeasibility in Optimization: Algorithms and Computational Methods
Fundamentals of Computerized Tomography: Image Reconstruction from Projections
Fundamentals of Computerized Tomography: Image Reconstruction from Projections
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Alternating Projection Methods
Alternating Projection Methods
Computational Optimization and Applications
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We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the scope of the family of SAP methods to allow iteration-index-dependent variable strings and weights and term such methods dynamic string-averaging projection (DSAP) methods. The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.