Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods
Abstract: 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.
Keywords: Dynamic string-averaging, projection methods, Perturbation resilience, fixed point, Hilbert space, metric projection, nonexpansive operator, superiorization method, variable strings, variable weights.
Category 1: Convex and Nonsmooth Optimization (Convex Optimization )
Category 2: Optimization Software and Modeling Systems (Parallel Algorithms )
Category 3: Applications -- Science and Engineering (Biomedical Applications )
Citation: Computational Optimization and Applications, accepted for publication. DOI:10.1007/s10589-012-9491-x.
Entry Submitted: 06/01/2012
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