Convergence and perturbation resilience of dynamic string-averaging projection methods

Yair Censor; Alexander J. Zaslavski

doi:10.1007/s10589-012-9491-x

Convergence and perturbation resilience of dynamic string-averaging projection methods

Yair Censor, Alexander J. Zaslavski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	65-76
Number of pages	12
Journal	Computational Optimization and Applications
Volume	54
Issue number	1
DOIs	https://doi.org/10.1007/s10589-012-9491-x
State	Published - Jan 2013

Bibliographical note

Funding Information:
We thank Chonghui Cheng and Rotem Karni for valuable discussion. We thank Abed Nasereddin and Idit Shiff from the Genomic Applications Laboratory, The Core Research Facility, The Faculty of Medicine - Ein Kerem, The Hebrew University of Jerusalem, Israel, for their professional advice and RNA-seq service. We thank Amina Jbara for guidance on scratch assay technique. We thank Chonghui Cheng for the hnRNP M plasmid and Alberto Kornblihtt for slow RNAPII plasmids. This work was in part supported by the Israeli Cancer Association, Alon Award by the Israeli Planning and Budgeting Committee (PBC), and the Israel Science Foundation (ISF 1154/17). The RNA-seq reagents were funded by a Core Laboratory Grant Program launched by Danyel Biotech, the authorized Illumina Channel Partner in Israel.

Keywords

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

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

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10.1007/s10589-012-9491-x

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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.",

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Convergence and perturbation resilience of dynamic string-averaging projection methods

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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