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Convergence and perturbation resilience of dynamic string-averaging projection methods

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  • Yair Censor

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  • Alexander Zaslavski

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    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. Copyright Springer Science+Business Media, LLC 2013

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    File URL: http://hdl.handle.net/10.1007/s10589-012-9491-x
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 54 (2013)
    Issue (Month): 1 (January)
    Pages: 65-76

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    Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:65-76

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Dynamic string-averaging; Projection methods; Perturbation resilience; Fixed point; Hilbert space; Metric projection; Nonexpansive operator; Superiorization method; Variable strings; Variable weights;

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    1. Yair Censor & Wei Chen & Patrick Combettes & Ran Davidi & Gabor Herman, 2012. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1065-1088, April.
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