Convergence and perturbation resilience of dynamic string‐averaging projection methods

Convergence and perturbation resilience of dynamic string‐averaging projection methods

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Article ID: iaor2013139
Volume: 54
Issue: 1
Start Page Number: 65
End Page Number: 76
Publication Date: Jan 2013
Journal: Computational Optimization and Applications
Authors: ,
Keywords: programming: convex, heuristics
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.

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