Convergence and perturbation resilience of dynamic string-averaging projection methods

Yair Censor, Alexander J. Zaslavski

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)65-76
Number of pages12
JournalComputational Optimization and Applications
Issue number1
StatePublished - 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.


  • 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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