Strict Fejér Monotonicity by Superiorization of Feasibility-Seeking Projection Methods

Yair Censor, Alexander J. Zaslavski

Research output: Contribution to journalArticlepeer-review


We consider the superiorization methodology, which can be thought of as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full-fledged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to the objective function value) to one returned by a feasibility-seeking only algorithm. Our main result reveals new information about the mathematical behavior of the superiorization methodology. We deal with a constrained minimization problem with a feasible region, which is the intersection of finitely many closed convex constraint sets, and use the dynamic string-averaging projection method, with variable strings and variable weights, as a feasibility-seeking algorithm. We show that any sequence, generated by the superiorized version of a dynamic string-averaging projection algorithm, not only converges to a feasible point but, additionally, also either its limit point solves the constrained minimization problem or the sequence is strictly Fejér monotone with respect to a subset of the solution set of the original problem.

Original languageEnglish
Pages (from-to)172-187
Number of pages16
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - 6 Apr 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.


  • Bounded perturbation resilience
  • Constrained minimization
  • Convex feasibility problem
  • Dynamic string-averaging projections
  • Strict Fejér monotonicity
  • Subgradients
  • Superiorization methodology
  • Superiorized version of an algorithm

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics


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